Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [500,2,Mod(7,500)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(500, base_ring=CyclotomicField(20))
chi = DirichletCharacter(H, H._module([10, 17]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("500.7");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 500 = 2^{2} \cdot 5^{3} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 500.l (of order \(20\), degree \(8\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(3.99252010106\) |
Analytic rank: | \(0\) |
Dimension: | \(96\) |
Relative dimension: | \(12\) over \(\Q(\zeta_{20})\) |
Twist minimal: | no (minimal twist has level 100) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{20}]$ |
Embedding invariants
Embedding label | 43.8 | ||
Character | \(\chi\) | \(=\) | 500.43 |
Dual form | 500.2.l.e.407.8 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/500\mathbb{Z}\right)^\times\).
\(n\) | \(251\) | \(377\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{19}{20}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.0976968 | + | 1.41083i | 0.0690820 | + | 0.997611i | ||||
\(3\) | 0.170251 | + | 0.0867473i | 0.0982946 | + | 0.0500836i | 0.502447 | − | 0.864608i | \(-0.332433\pi\) |
−0.404152 | + | 0.914692i | \(0.632433\pi\) | |||||||
\(4\) | −1.98091 | + | 0.275668i | −0.990455 | + | 0.137834i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −0.105753 | + | 0.248671i | −0.0431735 | + | 0.101520i | ||||
\(7\) | −1.89427 | − | 1.89427i | −0.715965 | − | 0.715965i | 0.251811 | − | 0.967776i | \(-0.418974\pi\) |
−0.967776 | + | 0.251811i | \(0.918974\pi\) | |||||||
\(8\) | −0.582451 | − | 2.76781i | −0.205927 | − | 0.978567i | ||||
\(9\) | −1.74190 | − | 2.39751i | −0.580632 | − | 0.799171i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.99934 | − | 4.12824i | 0.904336 | − | 1.24471i | −0.0647283 | − | 0.997903i | \(-0.520618\pi\) |
0.969064 | − | 0.246809i | \(-0.0793819\pi\) | |||||||
\(12\) | −0.361166 | − | 0.124906i | −0.104260 | − | 0.0360572i | ||||
\(13\) | 2.73586 | + | 0.433317i | 0.758790 | + | 0.120181i | 0.523828 | − | 0.851824i | \(-0.324503\pi\) |
0.234962 | + | 0.972005i | \(0.424503\pi\) | |||||||
\(14\) | 2.48743 | − | 2.85756i | 0.664795 | − | 0.763715i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 3.84801 | − | 1.09215i | 0.962004 | − | 0.273037i | ||||
\(17\) | 2.12318 | + | 4.16697i | 0.514947 | + | 1.01064i | 0.991329 | + | 0.131402i | \(0.0419477\pi\) |
−0.476383 | + | 0.879238i | \(0.658052\pi\) | |||||||
\(18\) | 3.21232 | − | 2.69176i | 0.757151 | − | 0.634453i | ||||
\(19\) | 1.55045 | − | 4.77181i | 0.355699 | − | 1.09473i | −0.599905 | − | 0.800072i | \(-0.704795\pi\) |
0.955603 | − | 0.294657i | \(-0.0952052\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.158179 | − | 0.486824i | −0.0345174 | − | 0.106234i | ||||
\(22\) | 6.11729 | + | 3.82826i | 1.30421 | + | 0.816188i | ||||
\(23\) | −4.41914 | + | 0.699923i | −0.921455 | + | 0.145944i | −0.599100 | − | 0.800675i | \(-0.704475\pi\) |
−0.322355 | + | 0.946619i | \(0.604475\pi\) | |||||||
\(24\) | 0.140937 | − | 0.521748i | 0.0287686 | − | 0.106501i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −0.344055 | + | 3.90218i | −0.0674747 | + | 0.765280i | ||||
\(27\) | −0.178255 | − | 1.12546i | −0.0343052 | − | 0.216595i | ||||
\(28\) | 4.27456 | + | 3.23018i | 0.807816 | + | 0.610447i | ||||
\(29\) | 0.211843 | − | 0.0688321i | 0.0393383 | − | 0.0127818i | −0.289282 | − | 0.957244i | \(-0.593416\pi\) |
0.328620 | + | 0.944462i | \(0.393416\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −7.01920 | − | 2.28068i | −1.26069 | − | 0.409622i | −0.398947 | − | 0.916974i | \(-0.630624\pi\) |
−0.861739 | + | 0.507352i | \(0.830624\pi\) | |||||||
\(32\) | 1.91678 | + | 5.32221i | 0.338842 | + | 0.940843i | ||||
\(33\) | 0.868756 | − | 0.442653i | 0.151231 | − | 0.0770560i | ||||
\(34\) | −5.67148 | + | 3.40256i | −0.972652 | + | 0.583533i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 4.11146 | + | 4.26907i | 0.685243 | + | 0.711512i | ||||
\(37\) | 0.684516 | − | 4.32186i | 0.112534 | − | 0.710510i | −0.865320 | − | 0.501220i | \(-0.832885\pi\) |
0.977854 | − | 0.209290i | \(-0.0671152\pi\) | |||||||
\(38\) | 6.88371 | + | 1.72125i | 1.11669 | + | 0.279223i | ||||
\(39\) | 0.428194 | + | 0.311101i | 0.0685659 | + | 0.0498160i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2.54404 | − | 1.84835i | 0.397312 | − | 0.288664i | −0.371133 | − | 0.928580i | \(-0.621031\pi\) |
0.768445 | + | 0.639915i | \(0.221031\pi\) | |||||||
\(42\) | 0.671374 | − | 0.270725i | 0.103595 | − | 0.0417738i | ||||
\(43\) | −2.68807 | + | 2.68807i | −0.409927 | + | 0.409927i | −0.881713 | − | 0.471786i | \(-0.843609\pi\) |
0.471786 | + | 0.881713i | \(0.343609\pi\) | |||||||
\(44\) | −4.80341 | + | 9.00450i | −0.724141 | + | 1.35748i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −1.41921 | − | 6.16630i | −0.209251 | − | 0.909171i | ||||
\(47\) | 3.99829 | − | 7.84709i | 0.583211 | − | 1.14462i | −0.391298 | − | 0.920264i | \(-0.627974\pi\) |
0.974508 | − | 0.224351i | \(-0.0720263\pi\) | |||||||
\(48\) | 0.749870 | + | 0.147866i | 0.108234 | + | 0.0213425i | ||||
\(49\) | 0.176489i | 0.0252127i | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0.893612i | 0.125131i | ||||||||
\(52\) | −5.53894 | − | 0.104174i | −0.768113 | − | 0.0144464i | ||||
\(53\) | −0.837124 | + | 1.64295i | −0.114988 | + | 0.225676i | −0.941327 | − | 0.337497i | \(-0.890420\pi\) |
0.826339 | + | 0.563173i | \(0.190420\pi\) | |||||||
\(54\) | 1.57042 | − | 0.361442i | 0.213707 | − | 0.0491861i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −4.13965 | + | 6.34628i | −0.553183 | + | 0.848057i | ||||
\(57\) | 0.677908 | − | 0.677908i | 0.0897912 | − | 0.0897912i | ||||
\(58\) | 0.117807 | + | 0.292151i | 0.0154688 | + | 0.0383614i | ||||
\(59\) | 7.33328 | − | 5.32794i | 0.954712 | − | 0.693639i | 0.00279513 | − | 0.999996i | \(-0.499110\pi\) |
0.951917 | + | 0.306357i | \(0.0991103\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.16375 | + | 0.845512i | 0.149003 | + | 0.108257i | 0.659789 | − | 0.751451i | \(-0.270646\pi\) |
−0.510786 | + | 0.859708i | \(0.670646\pi\) | |||||||
\(62\) | 2.53191 | − | 10.1258i | 0.321552 | − | 1.28597i | ||||
\(63\) | −1.24191 | + | 7.84114i | −0.156467 | + | 0.987891i | ||||
\(64\) | −7.32150 | + | 3.22422i | −0.915188 | + | 0.403028i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0.709385 | + | 1.18243i | 0.0873193 | + | 0.145546i | ||||
\(67\) | −3.01313 | + | 1.53527i | −0.368113 | + | 0.187563i | −0.628255 | − | 0.778007i | \(-0.716231\pi\) |
0.260142 | + | 0.965570i | \(0.416231\pi\) | |||||||
\(68\) | −5.35453 | − | 7.66911i | −0.649332 | − | 0.930016i | ||||
\(69\) | −0.813081 | − | 0.264186i | −0.0978834 | − | 0.0318043i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 5.45415 | − | 1.77216i | 0.647288 | − | 0.210317i | 0.0330703 | − | 0.999453i | \(-0.489471\pi\) |
0.614218 | + | 0.789136i | \(0.289471\pi\) | |||||||
\(72\) | −5.62128 | + | 6.21766i | −0.662475 | + | 0.732759i | ||||
\(73\) | −0.00296414 | − | 0.0187149i | −0.000346927 | − | 0.00219041i | 0.987514 | − | 0.157530i | \(-0.0503530\pi\) |
−0.987861 | + | 0.155339i | \(0.950353\pi\) | |||||||
\(74\) | 6.16431 | + | 0.543507i | 0.716586 | + | 0.0631814i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −1.75588 | + | 9.87994i | −0.201413 | + | 1.13331i | ||||
\(77\) | −13.5015 | + | 2.13843i | −1.53864 | + | 0.243697i | ||||
\(78\) | −0.397079 | + | 0.634505i | −0.0449604 | + | 0.0718435i | ||||
\(79\) | 2.08434 | + | 6.41493i | 0.234506 | + | 0.721736i | 0.997187 | + | 0.0749601i | \(0.0238830\pi\) |
−0.762680 | + | 0.646776i | \(0.776117\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −2.68002 | + | 8.24826i | −0.297780 | + | 0.916474i | ||||
\(82\) | 2.85627 | + | 3.40864i | 0.315422 | + | 0.376422i | ||||
\(83\) | −1.52629 | − | 2.99552i | −0.167532 | − | 0.328801i | 0.791942 | − | 0.610596i | \(-0.209070\pi\) |
−0.959475 | + | 0.281795i | \(0.909070\pi\) | |||||||
\(84\) | 0.447539 | + | 0.920749i | 0.0488305 | + | 0.100462i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −4.05504 | − | 3.52981i | −0.437266 | − | 0.380629i | ||||
\(87\) | 0.0420376 | + | 0.00665810i | 0.00450690 | + | 0.000713823i | ||||
\(88\) | −13.1731 | − | 5.89710i | −1.40426 | − | 0.628633i | ||||
\(89\) | 0.509284 | − | 0.700969i | 0.0539840 | − | 0.0743026i | −0.781172 | − | 0.624316i | \(-0.785378\pi\) |
0.835156 | + | 0.550014i | \(0.185378\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −4.36162 | − | 6.00326i | −0.457222 | − | 0.629313i | ||||
\(92\) | 8.56098 | − | 2.60470i | 0.892544 | − | 0.271559i | ||||
\(93\) | −0.997185 | − | 0.997185i | −0.103403 | − | 0.103403i | ||||
\(94\) | 11.4616 | + | 4.87429i | 1.18217 | + | 0.502745i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −0.135354 | + | 1.07239i | −0.0138145 | + | 0.109450i | ||||
\(97\) | 9.96296 | + | 5.07638i | 1.01158 | + | 0.515428i | 0.879545 | − | 0.475816i | \(-0.157847\pi\) |
0.132040 | + | 0.991244i | \(0.457847\pi\) | |||||||
\(98\) | −0.248997 | + | 0.0172424i | −0.0251525 | + | 0.00174175i | ||||
\(99\) | −15.1221 | −1.51982 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −11.8084 | −1.17498 | −0.587489 | − | 0.809232i | \(-0.699884\pi\) | ||||
−0.587489 | + | 0.809232i | \(0.699884\pi\) | |||||||
\(102\) | −1.26074 | + | 0.0873030i | −0.124832 | + | 0.00864429i | ||||
\(103\) | 1.72871 | + | 0.880821i | 0.170335 | + | 0.0867899i | 0.537079 | − | 0.843532i | \(-0.319528\pi\) |
−0.366744 | + | 0.930322i | \(0.619528\pi\) | |||||||
\(104\) | −0.394164 | − | 7.82471i | −0.0386509 | − | 0.767276i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −2.39971 | − | 1.02053i | −0.233081 | − | 0.0991230i | ||||
\(107\) | −8.09772 | − | 8.09772i | −0.782836 | − | 0.782836i | 0.197472 | − | 0.980308i | \(-0.436727\pi\) |
−0.980308 | + | 0.197472i | \(0.936727\pi\) | |||||||
\(108\) | 0.663361 | + | 2.18029i | 0.0638319 | + | 0.209799i | ||||
\(109\) | 9.13259 | + | 12.5699i | 0.874743 | + | 1.20398i | 0.977849 | + | 0.209310i | \(0.0671219\pi\) |
−0.103106 | + | 0.994670i | \(0.532878\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0.491450 | − | 0.676422i | 0.0466463 | − | 0.0642032i | ||||
\(112\) | −9.35798 | − | 5.22035i | −0.884246 | − | 0.493276i | ||||
\(113\) | −8.00964 | − | 1.26860i | −0.753483 | − | 0.119340i | −0.232135 | − | 0.972684i | \(-0.574571\pi\) |
−0.521349 | + | 0.853344i | \(0.674571\pi\) | |||||||
\(114\) | 1.02265 | + | 0.890188i | 0.0957796 | + | 0.0833737i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −0.400668 | + | 0.194749i | −0.0372011 | + | 0.0180820i | ||||
\(117\) | −3.72669 | − | 7.31405i | −0.344533 | − | 0.676184i | ||||
\(118\) | 8.23328 | + | 9.82552i | 0.757935 | + | 0.904513i | ||||
\(119\) | 3.87149 | − | 11.9152i | 0.354899 | − | 1.09227i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −4.64713 | − | 14.3024i | −0.422467 | − | 1.30022i | ||||
\(122\) | −1.07918 | + | 1.72446i | −0.0977047 | + | 0.156125i | ||||
\(123\) | 0.593466 | − | 0.0939957i | 0.0535110 | − | 0.00847531i | ||||
\(124\) | 14.5331 | + | 2.58285i | 1.30511 | + | 0.231947i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −11.1839 | − | 0.986083i | −0.996340 | − | 0.0878472i | ||||
\(127\) | 2.51108 | + | 15.8543i | 0.222822 | + | 1.40684i | 0.804755 | + | 0.593608i | \(0.202297\pi\) |
−0.581932 | + | 0.813237i | \(0.697703\pi\) | |||||||
\(128\) | −5.26413 | − | 10.0144i | −0.465288 | − | 0.885159i | ||||
\(129\) | −0.690830 | + | 0.224464i | −0.0608242 | + | 0.0197630i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 12.9418 | + | 4.20505i | 1.13073 | + | 0.367397i | 0.813854 | − | 0.581069i | \(-0.197365\pi\) |
0.316878 | + | 0.948466i | \(0.397365\pi\) | |||||||
\(132\) | −1.59890 | + | 1.11634i | −0.139167 | + | 0.0971653i | ||||
\(133\) | −11.9761 | + | 6.10210i | −1.03846 | + | 0.529119i | ||||
\(134\) | −2.46038 | − | 4.10104i | −0.212545 | − | 0.354276i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 10.2967 | − | 8.30361i | 0.882937 | − | 0.712028i | ||||
\(137\) | 2.95587 | − | 18.6626i | 0.252537 | − | 1.59445i | −0.456790 | − | 0.889575i | \(-0.651001\pi\) |
0.709327 | − | 0.704880i | \(-0.248999\pi\) | |||||||
\(138\) | 0.293287 | − | 1.17293i | 0.0249663 | − | 0.0998467i | ||||
\(139\) | 5.89560 | + | 4.28340i | 0.500058 | + | 0.363313i | 0.809039 | − | 0.587755i | \(-0.199988\pi\) |
−0.308981 | + | 0.951068i | \(0.599988\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1.36143 | − | 0.989135i | 0.114653 | − | 0.0833002i | ||||
\(142\) | 3.03308 | + | 7.52177i | 0.254530 | + | 0.631213i | ||||
\(143\) | 9.99461 | − | 9.99461i | 0.835792 | − | 0.835792i | ||||
\(144\) | −9.32128 | − | 7.32326i | −0.776773 | − | 0.610272i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0.0261140 | − | 0.00601030i | 0.00216121 | − | 0.000497416i | ||||
\(147\) | −0.0153100 | + | 0.0300475i | −0.00126274 | + | 0.00247828i | ||||
\(148\) | −0.164565 | + | 8.74992i | −0.0135272 | + | 0.719239i | ||||
\(149\) | 2.12851i | 0.174375i | 0.996192 | + | 0.0871873i | \(0.0277879\pi\) | ||||
−0.996192 | + | 0.0871873i | \(0.972212\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 6.10369i | 0.496712i | 0.968669 | + | 0.248356i | \(0.0798902\pi\) | ||||
−0.968669 | + | 0.248356i | \(0.920110\pi\) | |||||||
\(152\) | −14.1105 | − | 1.51202i | −1.14451 | − | 0.122641i | ||||
\(153\) | 6.29202 | − | 12.3488i | 0.508680 | − | 0.998340i | ||||
\(154\) | −4.33603 | − | 18.8395i | −0.349408 | − | 1.51813i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −0.933975 | − | 0.498224i | −0.0747778 | − | 0.0398899i | ||||
\(157\) | −11.4802 | + | 11.4802i | −0.916218 | + | 0.916218i | −0.996752 | − | 0.0805335i | \(-0.974338\pi\) |
0.0805335 | + | 0.996752i | \(0.474338\pi\) | |||||||
\(158\) | −8.84677 | + | 3.56737i | −0.703811 | + | 0.283805i | ||||
\(159\) | −0.285043 | + | 0.207096i | −0.0226054 | + | 0.0164238i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 9.69687 | + | 7.04519i | 0.764221 | + | 0.555239i | ||||
\(162\) | −11.8988 | − | 2.97524i | −0.934856 | − | 0.233757i | ||||
\(163\) | 1.23758 | − | 7.81379i | 0.0969349 | − | 0.612023i | −0.890620 | − | 0.454748i | \(-0.849729\pi\) |
0.987555 | − | 0.157275i | \(-0.0502708\pi\) | |||||||
\(164\) | −4.52998 | + | 4.36273i | −0.353732 | + | 0.340672i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 4.07707 | − | 2.44600i | 0.316442 | − | 0.189846i | ||||
\(167\) | −12.0426 | + | 6.13600i | −0.931883 | + | 0.474818i | −0.852910 | − | 0.522059i | \(-0.825164\pi\) |
−0.0789735 | + | 0.996877i | \(0.525164\pi\) | |||||||
\(168\) | −1.25530 | + | 0.721358i | −0.0968487 | + | 0.0556540i | ||||
\(169\) | −5.06658 | − | 1.64623i | −0.389737 | − | 0.126633i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −14.1412 | + | 4.59476i | −1.08141 | + | 0.351370i | ||||
\(172\) | 4.58381 | − | 6.06584i | 0.349512 | − | 0.462516i | ||||
\(173\) | 0.171594 | + | 1.08340i | 0.0130460 | + | 0.0823695i | 0.993352 | − | 0.115114i | \(-0.0367232\pi\) |
−0.980306 | + | 0.197483i | \(0.936723\pi\) | |||||||
\(174\) | −0.00528654 | + | 0.0599586i | −0.000400772 | + | 0.00454545i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 7.03287 | − | 19.1613i | 0.530122 | − | 1.44433i | ||||
\(177\) | 1.71068 | − | 0.270946i | 0.128583 | − | 0.0203655i | ||||
\(178\) | 1.03871 | + | 0.650033i | 0.0778544 | + | 0.0487220i | ||||
\(179\) | 7.45601 | + | 22.9472i | 0.557289 | + | 1.71516i | 0.689822 | + | 0.723979i | \(0.257689\pi\) |
−0.132533 | + | 0.991179i | \(0.542311\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2.15964 | + | 6.64670i | −0.160525 | + | 0.494045i | −0.998679 | − | 0.0513890i | \(-0.983635\pi\) |
0.838154 | + | 0.545434i | \(0.183635\pi\) | |||||||
\(182\) | 8.04349 | − | 6.74003i | 0.596223 | − | 0.499604i | ||||
\(183\) | 0.124784 | + | 0.244901i | 0.00922426 | + | 0.0181036i | ||||
\(184\) | 4.51119 | + | 11.8237i | 0.332569 | + | 0.871652i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 1.30944 | − | 1.50429i | 0.0960130 | − | 0.110300i | ||||
\(187\) | 23.5704 | + | 3.73319i | 1.72364 | + | 0.272998i | ||||
\(188\) | −5.75707 | + | 16.6466i | −0.419877 | + | 1.21408i | ||||
\(189\) | −1.79426 | + | 2.46958i | −0.130513 | + | 0.179636i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 9.26511 | + | 12.7523i | 0.670400 | + | 0.922727i | 0.999769 | − | 0.0214746i | \(-0.00683611\pi\) |
−0.329369 | + | 0.944201i | \(0.606836\pi\) | |||||||
\(192\) | −1.52619 | − | 0.0861932i | −0.110143 | − | 0.00622046i | ||||
\(193\) | 6.44920 | + | 6.44920i | 0.464223 | + | 0.464223i | 0.900037 | − | 0.435814i | \(-0.143539\pi\) |
−0.435814 | + | 0.900037i | \(0.643539\pi\) | |||||||
\(194\) | −6.18859 | + | 14.5520i | −0.444315 | + | 1.04478i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −0.0486524 | − | 0.349609i | −0.00347517 | − | 0.0249721i | ||||
\(197\) | 5.09406 | + | 2.59555i | 0.362936 | + | 0.184925i | 0.625943 | − | 0.779869i | \(-0.284714\pi\) |
−0.263007 | + | 0.964794i | \(0.584714\pi\) | |||||||
\(198\) | −1.47738 | − | 21.3347i | −0.104993 | − | 1.51619i | ||||
\(199\) | −24.6399 | −1.74668 | −0.873338 | − | 0.487115i | \(-0.838049\pi\) | ||||
−0.873338 | + | 0.487115i | \(0.838049\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −0.646170 | −0.0455773 | ||||||||
\(202\) | −1.15364 | − | 16.6597i | −0.0811699 | − | 1.17217i | ||||
\(203\) | −0.531674 | − | 0.270901i | −0.0373162 | − | 0.0190136i | ||||
\(204\) | −0.246340 | − | 1.77017i | −0.0172473 | − | 0.123936i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −1.07380 | + | 2.52498i | −0.0748155 | + | 0.175923i | ||||
\(207\) | 9.37576 | + | 9.37576i | 0.651660 | + | 0.651660i | ||||
\(208\) | 11.0009 | − | 1.32055i | 0.762773 | − | 0.0915636i | ||||
\(209\) | −15.0488 | − | 20.7129i | −1.04095 | − | 1.43274i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −11.6703 | + | 16.0628i | −0.803419 | + | 1.10581i | 0.188886 | + | 0.981999i | \(0.439512\pi\) |
−0.992306 | + | 0.123813i | \(0.960488\pi\) | |||||||
\(212\) | 1.20536 | − | 3.48530i | 0.0827845 | − | 0.239372i | ||||
\(213\) | 1.08231 | + | 0.171420i | 0.0741584 | + | 0.0117455i | ||||
\(214\) | 10.6334 | − | 12.2157i | 0.726886 | − | 0.835046i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −3.01123 | + | 1.14890i | −0.204888 | + | 0.0781728i | ||||
\(217\) | 8.97603 | + | 17.6165i | 0.609333 | + | 1.19588i | ||||
\(218\) | −16.8419 | + | 14.1126i | −1.14068 | + | 0.955827i | ||||
\(219\) | 0.00111881 | − | 0.00344336i | 7.56025e−5 | − | 0.000232681i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 4.00309 | + | 12.3203i | 0.269277 | + | 0.828750i | ||||
\(222\) | 1.00233 | + | 0.627270i | 0.0672722 | + | 0.0420996i | ||||
\(223\) | 11.4317 | − | 1.81060i | 0.765524 | − | 0.121247i | 0.238552 | − | 0.971130i | \(-0.423327\pi\) |
0.526972 | + | 0.849883i | \(0.323327\pi\) | |||||||
\(224\) | 6.45080 | − | 13.7126i | 0.431012 | − | 0.916210i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 1.00727 | − | 11.4242i | 0.0670028 | − | 0.759928i | ||||
\(227\) | 2.42897 | + | 15.3359i | 0.161216 | + | 1.01788i | 0.927077 | + | 0.374872i | \(0.122313\pi\) |
−0.765861 | + | 0.643007i | \(0.777687\pi\) | |||||||
\(228\) | −1.15600 | + | 1.52975i | −0.0765579 | + | 0.101310i | ||||
\(229\) | 16.0312 | − | 5.20884i | 1.05937 | − | 0.344210i | 0.273030 | − | 0.962006i | \(-0.411974\pi\) |
0.786339 | + | 0.617796i | \(0.211974\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −2.48416 | − | 0.807152i | −0.163446 | − | 0.0531067i | ||||
\(232\) | −0.313902 | − | 0.546250i | −0.0206087 | − | 0.0358631i | ||||
\(233\) | 26.0233 | − | 13.2595i | 1.70484 | − | 0.868660i | 0.720267 | − | 0.693697i | \(-0.244019\pi\) |
0.984575 | − | 0.174963i | \(-0.0559806\pi\) | |||||||
\(234\) | 9.95483 | − | 5.97231i | 0.650768 | − | 0.390422i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −13.0578 | + | 12.5757i | −0.849992 | + | 0.818610i | ||||
\(237\) | −0.201617 | + | 1.27296i | −0.0130964 | + | 0.0826876i | ||||
\(238\) | 17.1886 | + | 4.29796i | 1.11417 | + | 0.278595i | ||||
\(239\) | −0.369981 | − | 0.268807i | −0.0239321 | − | 0.0173877i | 0.575755 | − | 0.817622i | \(-0.304708\pi\) |
−0.599687 | + | 0.800235i | \(0.704708\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 17.6697 | − | 12.8378i | 1.13820 | − | 0.826953i | 0.151335 | − | 0.988483i | \(-0.451643\pi\) |
0.986868 | + | 0.161530i | \(0.0516429\pi\) | |||||||
\(242\) | 19.7243 | − | 7.95364i | 1.26793 | − | 0.511279i | ||||
\(243\) | −3.58901 | + | 3.58901i | −0.230235 | + | 0.230235i | ||||
\(244\) | −2.53836 | − | 1.35408i | −0.162502 | − | 0.0866858i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0.190592 | + | 0.828099i | 0.0121517 | + | 0.0527977i | ||||
\(247\) | 6.30953 | − | 12.3832i | 0.401466 | − | 0.787921i | ||||
\(248\) | −2.22413 | + | 20.7562i | −0.141233 | + | 1.31802i | ||||
\(249\) | − | 0.642393i | − | 0.0407100i | ||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 5.42259i | − | 0.342271i | −0.985248 | − | 0.171135i | \(-0.945256\pi\) | ||
0.985248 | − | 0.171135i | \(-0.0547436\pi\) | |||||||
\(252\) | 0.298570 | − | 15.8750i | 0.0188082 | − | 1.00003i | ||||
\(253\) | −10.3651 | + | 20.3426i | −0.651647 | + | 1.27893i | ||||
\(254\) | −22.1225 | + | 5.09164i | −1.38809 | + | 0.319478i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 13.6144 | − | 8.40520i | 0.850902 | − | 0.525325i | ||||
\(257\) | 8.02192 | − | 8.02192i | 0.500394 | − | 0.500394i | −0.411166 | − | 0.911560i | \(-0.634879\pi\) |
0.911560 | + | 0.411166i | \(0.134879\pi\) | |||||||
\(258\) | −0.384174 | − | 0.952717i | −0.0239176 | − | 0.0593136i | ||||
\(259\) | −9.48341 | + | 6.89010i | −0.589271 | + | 0.428130i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −0.534035 | − | 0.387999i | −0.0330559 | − | 0.0240165i | ||||
\(262\) | −4.66826 | + | 18.6696i | −0.288406 | + | 1.15341i | ||||
\(263\) | 3.11132 | − | 19.6441i | 0.191852 | − | 1.21131i | −0.684275 | − | 0.729224i | \(-0.739881\pi\) |
0.876127 | − | 0.482081i | \(-0.160119\pi\) | |||||||
\(264\) | −1.73119 | − | 2.14672i | −0.106547 | − | 0.132122i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −9.77908 | − | 16.3001i | −0.599594 | − | 0.999422i | ||||
\(267\) | 0.147513 | − | 0.0751618i | 0.00902767 | − | 0.00459983i | ||||
\(268\) | 5.54552 | − | 3.87185i | 0.338747 | − | 0.236511i | ||||
\(269\) | 9.63789 | + | 3.13154i | 0.587633 | + | 0.190933i | 0.587717 | − | 0.809067i | \(-0.300027\pi\) |
−8.44003e−5 | 1.00000i | \(0.500027\pi\) | ||||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.79674 | − | 0.583795i | 0.109144 | − | 0.0354630i | −0.253936 | − | 0.967221i | \(-0.581725\pi\) |
0.363080 | + | 0.931758i | \(0.381725\pi\) | |||||||
\(272\) | 12.7210 | + | 13.7158i | 0.771322 | + | 0.831640i | ||||
\(273\) | −0.221805 | − | 1.40042i | −0.0134243 | − | 0.0847574i | ||||
\(274\) | 26.6186 | + | 2.34696i | 1.60809 | + | 0.141785i | ||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 1.68347 | + | 0.299188i | 0.101333 | + | 0.0180090i | ||||
\(277\) | 11.3089 | − | 1.79116i | 0.679488 | − | 0.107620i | 0.192855 | − | 0.981227i | \(-0.438225\pi\) |
0.486632 | + | 0.873607i | \(0.338225\pi\) | |||||||
\(278\) | −5.46719 | + | 8.73619i | −0.327900 | + | 0.523962i | ||||
\(279\) | 6.75877 | + | 20.8013i | 0.404637 | + | 1.24534i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 7.15917 | − | 22.0337i | 0.427080 | − | 1.31442i | −0.473908 | − | 0.880574i | \(-0.657157\pi\) |
0.900988 | − | 0.433844i | \(-0.142843\pi\) | |||||||
\(282\) | 1.52851 | + | 1.82411i | 0.0910217 | + | 0.108624i | ||||
\(283\) | 8.65065 | + | 16.9779i | 0.514228 | + | 1.00923i | 0.991455 | + | 0.130449i | \(0.0416420\pi\) |
−0.477227 | + | 0.878780i | \(0.658358\pi\) | |||||||
\(284\) | −10.3157 | + | 5.01403i | −0.612121 | + | 0.297528i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 15.0772 | + | 13.1243i | 0.891533 | + | 0.776057i | ||||
\(287\) | −8.32036 | − | 1.31782i | −0.491135 | − | 0.0777882i | ||||
\(288\) | 9.42125 | − | 13.8662i | 0.555153 | − | 0.817076i | ||||
\(289\) | −2.86343 | + | 3.94118i | −0.168437 | + | 0.231834i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1.25584 | + | 1.72852i | 0.0736188 | + | 0.101328i | ||||
\(292\) | 0.0110308 | + | 0.0362553i | 0.000645528 | + | 0.00212168i | ||||
\(293\) | −9.23047 | − | 9.23047i | −0.539250 | − | 0.539250i | 0.384059 | − | 0.923309i | \(-0.374526\pi\) |
−0.923309 | + | 0.384059i | \(0.874526\pi\) | |||||||
\(294\) | −0.0438878 | − | 0.0186643i | −0.00255959 | − | 0.00108852i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −12.3608 | + | 0.622665i | −0.718455 | + | 0.0361916i | ||||
\(297\) | −5.18082 | − | 2.63976i | −0.300621 | − | 0.153174i | ||||
\(298\) | −3.00298 | + | 0.207949i | −0.173958 | + | 0.0120462i | ||||
\(299\) | −12.3934 | −0.716731 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 10.1838 | 0.586986 | ||||||||
\(302\) | −8.61130 | + | 0.596311i | −0.495525 | + | 0.0343138i | ||||
\(303\) | −2.01039 | − | 1.02435i | −0.115494 | − | 0.0588472i | ||||
\(304\) | 0.754653 | − | 20.0553i | 0.0432823 | − | 1.15025i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 18.0368 | + | 7.67056i | 1.03110 | + | 0.438497i | ||||
\(307\) | −9.17187 | − | 9.17187i | −0.523466 | − | 0.523466i | 0.395150 | − | 0.918616i | \(-0.370692\pi\) |
−0.918616 | + | 0.395150i | \(0.870692\pi\) | |||||||
\(308\) | 26.1559 | − | 7.95799i | 1.49037 | − | 0.453449i | ||||
\(309\) | 0.217906 | + | 0.299922i | 0.0123962 | + | 0.0170619i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 2.44643 | − | 3.36722i | 0.138724 | − | 0.190938i | −0.734002 | − | 0.679147i | \(-0.762350\pi\) |
0.872726 | + | 0.488209i | \(0.162350\pi\) | |||||||
\(312\) | 0.611666 | − | 1.36636i | 0.0346288 | − | 0.0773548i | ||||
\(313\) | 22.1282 | + | 3.50477i | 1.25076 | + | 0.198101i | 0.746462 | − | 0.665427i | \(-0.231751\pi\) |
0.504300 | + | 0.863529i | \(0.331751\pi\) | |||||||
\(314\) | −17.3182 | − | 15.0751i | −0.977324 | − | 0.850735i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −5.89727 | − | 12.1328i | −0.331748 | − | 0.682524i | ||||
\(317\) | −2.85992 | − | 5.61291i | −0.160629 | − | 0.315252i | 0.796639 | − | 0.604456i | \(-0.206609\pi\) |
−0.957268 | + | 0.289204i | \(0.906609\pi\) | |||||||
\(318\) | −0.320026 | − | 0.381916i | −0.0179462 | − | 0.0214168i | ||||
\(319\) | 0.351235 | − | 1.08099i | 0.0196654 | − | 0.0605239i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −0.676191 | − | 2.08110i | −0.0377413 | − | 0.116156i | ||||
\(322\) | −8.99225 | + | 14.3690i | −0.501118 | + | 0.800752i | ||||
\(323\) | 23.1759 | − | 3.67070i | 1.28954 | − | 0.204243i | ||||
\(324\) | 3.03510 | − | 17.0779i | 0.168617 | − | 0.948771i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 11.1449 | + | 0.982643i | 0.617257 | + | 0.0544235i | ||||
\(327\) | 0.464426 | + | 2.93227i | 0.0256828 | + | 0.162155i | ||||
\(328\) | −6.59766 | − | 5.96484i | −0.364295 | − | 0.329353i | ||||
\(329\) | −22.4383 | + | 7.29065i | −1.23706 | + | 0.401946i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 15.4106 | + | 5.00720i | 0.847042 | + | 0.275221i | 0.700206 | − | 0.713940i | \(-0.253091\pi\) |
0.146835 | + | 0.989161i | \(0.453091\pi\) | |||||||
\(332\) | 3.84922 | + | 5.51311i | 0.211253 | + | 0.302571i | ||||
\(333\) | −11.5541 | + | 5.88710i | −0.633159 | + | 0.322611i | ||||
\(334\) | −9.83341 | − | 16.3906i | −0.538060 | − | 0.896855i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −1.14036 | − | 1.70055i | −0.0622116 | − | 0.0927726i | ||||
\(337\) | −3.16369 | + | 19.9748i | −0.172337 | + | 1.08809i | 0.738174 | + | 0.674610i | \(0.235688\pi\) |
−0.910511 | + | 0.413484i | \(0.864312\pi\) | |||||||
\(338\) | 1.82757 | − | 7.30894i | 0.0994069 | − | 0.397554i | ||||
\(339\) | −1.25360 | − | 0.910796i | −0.0680864 | − | 0.0494676i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −30.4682 | + | 22.1364i | −1.64995 | + | 1.19876i | ||||
\(342\) | −7.86399 | − | 19.5020i | −0.425236 | − | 1.05455i | ||||
\(343\) | −12.9255 | + | 12.9255i | −0.697914 | + | 0.697914i | ||||
\(344\) | 9.00572 | + | 5.87439i | 0.485556 | + | 0.316726i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −1.51174 | + | 0.347935i | −0.0812714 | + | 0.0187051i | ||||
\(347\) | −2.63206 | + | 5.16571i | −0.141296 | + | 0.277310i | −0.950800 | − | 0.309805i | \(-0.899736\pi\) |
0.809504 | + | 0.587115i | \(0.199736\pi\) | |||||||
\(348\) | −0.0851081 | − | 0.00160068i | −0.00456227 | − | 8.58056e-5i | ||||
\(349\) | 0.0528810i | 0.00283065i | 0.999999 | + | 0.00141533i | \(0.000450513\pi\) | ||||
−0.999999 | + | 0.00141533i | \(0.999549\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − | 3.15634i | − | 0.168473i | ||||||
\(352\) | 27.7205 | + | 8.05022i | 1.47751 | + | 0.429078i | ||||
\(353\) | 1.86927 | − | 3.66865i | 0.0994913 | − | 0.195263i | −0.835896 | − | 0.548888i | \(-0.815051\pi\) |
0.935387 | + | 0.353626i | \(0.115051\pi\) | |||||||
\(354\) | 0.549388 | + | 2.38702i | 0.0291996 | + | 0.126869i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −0.815611 | + | 1.52895i | −0.0432273 | + | 0.0810342i | ||||
\(357\) | 1.69274 | − | 1.69274i | 0.0895893 | − | 0.0895893i | ||||
\(358\) | −31.6463 | + | 12.7611i | −1.67256 | + | 0.674444i | ||||
\(359\) | 22.3556 | − | 16.2423i | 1.17989 | − | 0.857237i | 0.187726 | − | 0.982221i | \(-0.439888\pi\) |
0.992159 | + | 0.124985i | \(0.0398882\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −4.99493 | − | 3.62903i | −0.262891 | − | 0.191002i | ||||
\(362\) | −9.58838 | − | 2.39754i | −0.503954 | − | 0.126012i | ||||
\(363\) | 0.449515 | − | 2.83813i | 0.0235934 | − | 0.148963i | ||||
\(364\) | 10.2949 | + | 10.6896i | 0.539599 | + | 0.560285i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −0.333325 | + | 0.199975i | −0.0174232 | + | 0.0104529i | ||||
\(367\) | −6.04885 | + | 3.08204i | −0.315747 | + | 0.160881i | −0.604681 | − | 0.796468i | \(-0.706699\pi\) |
0.288934 | + | 0.957349i | \(0.406699\pi\) | |||||||
\(368\) | −16.2405 | + | 7.51967i | −0.846595 | + | 0.391990i | ||||
\(369\) | −8.86290 | − | 2.87973i | −0.461384 | − | 0.149913i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 4.69792 | − | 1.52645i | 0.243904 | − | 0.0792492i | ||||
\(372\) | 2.25023 | + | 1.70044i | 0.116669 | + | 0.0881639i | ||||
\(373\) | −1.79701 | − | 11.3458i | −0.0930454 | − | 0.587466i | −0.989523 | − | 0.144376i | \(-0.953882\pi\) |
0.896477 | − | 0.443089i | \(-0.146118\pi\) | |||||||
\(374\) | −2.96416 | + | 33.6187i | −0.153273 | + | 1.73838i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −24.0480 | − | 6.49595i | −1.24018 | − | 0.335003i | ||||
\(377\) | 0.609399 | − | 0.0965194i | 0.0313857 | − | 0.00497100i | ||||
\(378\) | −3.65947 | − | 2.29013i | −0.188223 | − | 0.117792i | ||||
\(379\) | −3.95657 | − | 12.1771i | −0.203235 | − | 0.625494i | −0.999781 | − | 0.0209157i | \(-0.993342\pi\) |
0.796546 | − | 0.604578i | \(-0.206658\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −0.947807 | + | 2.91705i | −0.0485576 | + | 0.149445i | ||||
\(382\) | −17.0863 | + | 14.3174i | −0.874210 | + | 0.732542i | ||||
\(383\) | −8.36780 | − | 16.4227i | −0.427575 | − | 0.839163i | −0.999818 | − | 0.0190788i | \(-0.993927\pi\) |
0.572243 | − | 0.820084i | \(-0.306073\pi\) | |||||||
\(384\) | −0.0274992 | − | 2.16162i | −0.00140331 | − | 0.110310i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −8.46869 | + | 9.72882i | −0.431045 | + | 0.495184i | ||||
\(387\) | 11.1270 | + | 1.76235i | 0.565618 | + | 0.0895851i | ||||
\(388\) | −21.1351 | − | 7.30939i | −1.07297 | − | 0.371078i | ||||
\(389\) | 14.6199 | − | 20.1226i | 0.741258 | − | 1.02025i | −0.257287 | − | 0.966335i | \(-0.582829\pi\) |
0.998545 | − | 0.0539190i | \(-0.0171713\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −12.2992 | − | 16.9284i | −0.621997 | − | 0.856105i | ||||
\(392\) | 0.488488 | − | 0.102796i | 0.0246724 | − | 0.00519199i | ||||
\(393\) | 1.83858 | + | 1.83858i | 0.0927443 | + | 0.0927443i | ||||
\(394\) | −3.16422 | + | 7.44045i | −0.159411 | + | 0.374844i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 29.9554 | − | 4.16867i | 1.50532 | − | 0.209483i | ||||
\(397\) | −24.8148 | − | 12.6438i | −1.24542 | − | 0.634574i | −0.298001 | − | 0.954566i | \(-0.596320\pi\) |
−0.947420 | + | 0.319992i | \(0.896320\pi\) | |||||||
\(398\) | −2.40724 | − | 34.7628i | −0.120664 | − | 1.74250i | ||||
\(399\) | −2.56828 | −0.128575 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 10.4612 | 0.522406 | 0.261203 | − | 0.965284i | \(-0.415881\pi\) | ||||
0.261203 | + | 0.965284i | \(0.415881\pi\) | |||||||
\(402\) | −0.0631287 | − | 0.911639i | −0.00314857 | − | 0.0454684i | ||||
\(403\) | −18.2153 | − | 9.28115i | −0.907368 | − | 0.462327i | ||||
\(404\) | 23.3914 | − | 3.25520i | 1.16376 | − | 0.161952i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0.330254 | − | 0.776571i | 0.0163903 | − | 0.0385405i | ||||
\(407\) | −15.7886 | − | 15.7886i | −0.782611 | − | 0.782611i | ||||
\(408\) | 2.47335 | − | 0.520485i | 0.122449 | − | 0.0257679i | ||||
\(409\) | 9.12365 | + | 12.5576i | 0.451136 | + | 0.620935i | 0.972641 | − | 0.232313i | \(-0.0746294\pi\) |
−0.521505 | + | 0.853248i | \(0.674629\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 2.12217 | − | 2.92092i | 0.104679 | − | 0.144078i | ||||
\(412\) | −3.66723 | − | 1.26828i | −0.180672 | − | 0.0624836i | ||||
\(413\) | −23.9837 | − | 3.79865i | −1.18016 | − | 0.186919i | ||||
\(414\) | −12.3117 | + | 14.1436i | −0.605086 | + | 0.695122i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 2.93783 | + | 15.3914i | 0.144039 | + | 0.754625i | ||||
\(417\) | 0.632159 | + | 1.24068i | 0.0309569 | + | 0.0607564i | ||||
\(418\) | 27.7523 | − | 23.2550i | 1.35741 | − | 1.13744i | ||||
\(419\) | 11.1568 | − | 34.3371i | 0.545045 | − | 1.67748i | −0.175838 | − | 0.984419i | \(-0.556264\pi\) |
0.720883 | − | 0.693056i | \(-0.243736\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 4.95128 | + | 15.2385i | 0.241311 | + | 0.742678i | 0.996221 | + | 0.0868504i | \(0.0276802\pi\) |
−0.754911 | + | 0.655828i | \(0.772320\pi\) | |||||||
\(422\) | −23.8022 | − | 14.8956i | −1.15867 | − | 0.725108i | ||||
\(423\) | −25.7781 | + | 4.08285i | −1.25337 | + | 0.198515i | ||||
\(424\) | 5.03495 | + | 1.36006i | 0.244519 | + | 0.0660504i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −0.136108 | + | 1.54370i | −0.00659446 | + | 0.0747926i | ||||
\(427\) | −0.602823 | − | 3.80607i | −0.0291726 | − | 0.184189i | ||||
\(428\) | 18.2731 | + | 13.8086i | 0.883266 | + | 0.667463i | ||||
\(429\) | 2.56860 | − | 0.834589i | 0.124013 | − | 0.0402943i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −6.40797 | − | 2.08208i | −0.308661 | − | 0.100290i | 0.150591 | − | 0.988596i | \(-0.451882\pi\) |
−0.459252 | + | 0.888306i | \(0.651882\pi\) | |||||||
\(432\) | −1.91510 | − | 4.13610i | −0.0921401 | − | 0.198998i | ||||
\(433\) | −9.39790 | + | 4.78847i | −0.451634 | + | 0.230119i | −0.664985 | − | 0.746857i | \(-0.731562\pi\) |
0.213351 | + | 0.976976i | \(0.431562\pi\) | |||||||
\(434\) | −23.9770 | + | 14.3848i | −1.15093 | + | 0.690491i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −21.5560 | − | 22.3823i | −1.03234 | − | 1.07192i | ||||
\(437\) | −3.51178 | + | 22.1725i | −0.167991 | + | 1.06065i | ||||
\(438\) | 0.00496732 | + | 0.00124206i | 0.000237347 | + | 5.93478e-5i | ||||
\(439\) | 8.47207 | + | 6.15532i | 0.404350 | + | 0.293778i | 0.771311 | − | 0.636459i | \(-0.219602\pi\) |
−0.366960 | + | 0.930237i | \(0.619602\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0.423135 | − | 0.307426i | 0.0201493 | − | 0.0146393i | ||||
\(442\) | −16.9908 | + | 6.85136i | −0.808168 | + | 0.325886i | ||||
\(443\) | 3.27124 | − | 3.27124i | 0.155421 | − | 0.155421i | −0.625113 | − | 0.780534i | \(-0.714947\pi\) |
0.780534 | + | 0.625113i | \(0.214947\pi\) | |||||||
\(444\) | −0.787050 | + | 1.47541i | −0.0373517 | + | 0.0700198i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 3.67131 | + | 15.9514i | 0.173841 | + | 0.755319i | ||||
\(447\) | −0.184643 | + | 0.362382i | −0.00873331 | + | 0.0171401i | ||||
\(448\) | 19.9764 | + | 7.76134i | 0.943797 | + | 0.366689i | ||||
\(449\) | 18.0931i | 0.853868i | 0.904283 | + | 0.426934i | \(0.140406\pi\) | ||||
−0.904283 | + | 0.426934i | \(0.859594\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 16.0463i | − | 0.755589i | ||||||
\(452\) | 16.2161 | + | 0.304986i | 0.762741 | + | 0.0143453i | ||||
\(453\) | −0.529479 | + | 1.03916i | −0.0248771 | + | 0.0488241i | ||||
\(454\) | −21.3991 | + | 4.92514i | −1.00431 | + | 0.231148i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −2.27117 | − | 1.48147i | −0.106357 | − | 0.0693762i | ||||
\(457\) | 23.4612 | − | 23.4612i | 1.09747 | − | 1.09747i | 0.102764 | − | 0.994706i | \(-0.467231\pi\) |
0.994706 | − | 0.102764i | \(-0.0327687\pi\) | |||||||
\(458\) | 8.91500 | + | 22.1084i | 0.416571 | + | 1.03306i | ||||
\(459\) | 4.31129 | − | 3.13234i | 0.201234 | − | 0.146205i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −26.1799 | − | 19.0208i | −1.21932 | − | 0.885887i | −0.223275 | − | 0.974755i | \(-0.571675\pi\) |
−0.996043 | + | 0.0888686i | \(0.971675\pi\) | |||||||
\(462\) | 0.896064 | − | 3.58359i | 0.0416887 | − | 0.166724i | ||||
\(463\) | −4.79718 | + | 30.2882i | −0.222944 | + | 1.40761i | 0.581481 | + | 0.813560i | \(0.302473\pi\) |
−0.804425 | + | 0.594054i | \(0.797527\pi\) | |||||||
\(464\) | 0.740002 | − | 0.496231i | 0.0343537 | − | 0.0230369i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 21.2494 | + | 35.4191i | 0.984359 | + | 1.64076i | ||||
\(467\) | −13.8884 | + | 7.07648i | −0.642677 | + | 0.327460i | −0.744777 | − | 0.667314i | \(-0.767444\pi\) |
0.102100 | + | 0.994774i | \(0.467444\pi\) | |||||||
\(468\) | 9.39850 | + | 13.4611i | 0.434446 | + | 0.622242i | ||||
\(469\) | 8.61588 | + | 2.79947i | 0.397844 | + | 0.129268i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −2.95039 | + | 0.958640i | −0.135947 | + | 0.0441718i | ||||
\(472\) | −19.0180 | − | 17.1938i | −0.875373 | − | 0.791410i | ||||
\(473\) | 3.03456 | + | 19.1594i | 0.139529 | + | 0.880952i | ||||
\(474\) | −1.81563 | − | 0.160084i | −0.0833948 | − | 0.00735291i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −4.38443 | + | 24.6702i | −0.200960 | + | 1.13076i | ||||
\(477\) | 5.39718 | − | 0.854829i | 0.247120 | − | 0.0391399i | ||||
\(478\) | 0.343096 | − | 0.548244i | 0.0156929 | − | 0.0250761i | ||||
\(479\) | −2.15249 | − | 6.62469i | −0.0983498 | − | 0.302690i | 0.889762 | − | 0.456424i | \(-0.150870\pi\) |
−0.988112 | + | 0.153734i | \(0.950870\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 3.74547 | − | 11.5274i | 0.170779 | − | 0.525604i | ||||
\(482\) | 19.8382 | + | 23.6748i | 0.903606 | + | 1.07836i | ||||
\(483\) | 1.03975 | + | 2.04063i | 0.0473104 | + | 0.0928519i | ||||
\(484\) | 13.1483 | + | 27.0507i | 0.597649 | + | 1.22958i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −5.41414 | − | 4.71287i | −0.245590 | − | 0.213780i | ||||
\(487\) | 20.5964 | + | 3.26215i | 0.933313 | + | 0.147822i | 0.604529 | − | 0.796583i | \(-0.293361\pi\) |
0.328784 | + | 0.944405i | \(0.393361\pi\) | |||||||
\(488\) | 1.66239 | − | 3.71350i | 0.0752528 | − | 0.168102i | ||||
\(489\) | 0.888525 | − | 1.22295i | 0.0401805 | − | 0.0553037i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 2.89183 | + | 3.98026i | 0.130506 | + | 0.179627i | 0.869269 | − | 0.494339i | \(-0.164590\pi\) |
−0.738763 | + | 0.673965i | \(0.764590\pi\) | |||||||
\(492\) | −1.14969 | + | 0.349797i | −0.0518321 | + | 0.0157700i | ||||
\(493\) | 0.736603 | + | 0.736603i | 0.0331749 | + | 0.0331749i | ||||
\(494\) | 18.0870 | + | 7.69191i | 0.813773 | + | 0.346076i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −29.5008 | − | 1.11007i | −1.32463 | − | 0.0498438i | ||||
\(497\) | −13.6886 | − | 6.97467i | −0.614016 | − | 0.312857i | ||||
\(498\) | 0.906310 | − | 0.0627597i | 0.0406127 | − | 0.00281233i | ||||
\(499\) | 19.8140 | 0.886994 | 0.443497 | − | 0.896276i | \(-0.353738\pi\) | ||||
0.443497 | + | 0.896276i | \(0.353738\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −2.58255 | −0.115380 | ||||||||
\(502\) | 7.65038 | − | 0.529770i | 0.341453 | − | 0.0236448i | ||||
\(503\) | 24.4770 | + | 12.4717i | 1.09138 | + | 0.556084i | 0.904575 | − | 0.426314i | \(-0.140188\pi\) |
0.186801 | + | 0.982398i | \(0.440188\pi\) | |||||||
\(504\) | 22.4261 | − | 1.12970i | 0.998939 | − | 0.0503208i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −29.7127 | − | 12.6360i | −1.32089 | − | 0.561739i | ||||
\(507\) | −0.719785 | − | 0.719785i | −0.0319668 | − | 0.0319668i | ||||
\(508\) | −9.34476 | − | 30.7138i | −0.414607 | − | 1.36270i | ||||
\(509\) | 8.04575 | + | 11.0740i | 0.356622 | + | 0.490847i | 0.949204 | − | 0.314663i | \(-0.101891\pi\) |
−0.592582 | + | 0.805510i | \(0.701891\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −0.0298360 | + | 0.0410658i | −0.00131987 | + | 0.00181664i | ||||
\(512\) | 13.1884 | + | 18.3866i | 0.582852 | + | 0.812578i | ||||
\(513\) | −5.64685 | − | 0.894374i | −0.249315 | − | 0.0394876i | ||||
\(514\) | 12.1013 | + | 10.5339i | 0.533767 | + | 0.464630i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 1.30659 | − | 0.635083i | 0.0575196 | − | 0.0279580i | ||||
\(517\) | −20.4024 | − | 40.0420i | −0.897298 | − | 1.76105i | ||||
\(518\) | −10.6473 | − | 12.7064i | −0.467815 | − | 0.558287i | ||||
\(519\) | −0.0647681 | + | 0.199336i | −0.00284300 | + | 0.00874987i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 1.41202 | + | 4.34576i | 0.0618618 | + | 0.190391i | 0.977211 | − | 0.212270i | \(-0.0680855\pi\) |
−0.915349 | + | 0.402661i | \(0.868085\pi\) | |||||||
\(522\) | 0.495229 | − | 0.791341i | 0.0216756 | − | 0.0346361i | ||||
\(523\) | −35.8180 | + | 5.67302i | −1.56621 | + | 0.248064i | −0.878437 | − | 0.477859i | \(-0.841413\pi\) |
−0.687776 | + | 0.725923i | \(0.741413\pi\) | |||||||
\(524\) | −26.7958 | − | 4.76219i | −1.17058 | − | 0.208037i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 28.0185 | + | 2.47039i | 1.22167 | + | 0.107714i | ||||
\(527\) | −5.39950 | − | 34.0911i | −0.235206 | − | 1.48503i | ||||
\(528\) | 2.85954 | − | 2.65214i | 0.124446 | − | 0.115420i | ||||
\(529\) | −2.83537 | + | 0.921267i | −0.123277 | + | 0.0400551i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −25.5476 | − | 8.30092i | −1.10867 | − | 0.360229i | ||||
\(532\) | 22.0413 | − | 15.3891i | 0.955613 | − | 0.667204i | ||||
\(533\) | 7.76106 | − | 3.95446i | 0.336169 | − | 0.171286i | ||||
\(534\) | 0.120452 | + | 0.200774i | 0.00521249 | + | 0.00868834i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 6.00433 | + | 7.44555i | 0.259347 | + | 0.321599i | ||||
\(537\) | −0.721217 | + | 4.55359i | −0.0311228 | + | 0.196502i | ||||
\(538\) | −3.47650 | + | 13.9034i | −0.149882 | + | 0.599419i | ||||
\(539\) | 0.728590 | + | 0.529352i | 0.0313826 | + | 0.0228008i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −23.6895 | + | 17.2114i | −1.01849 | + | 0.739976i | −0.965973 | − | 0.258644i | \(-0.916724\pi\) |
−0.0525174 | + | 0.998620i | \(0.516724\pi\) | |||||||
\(542\) | 0.999174 | + | 2.47786i | 0.0429182 | + | 0.106433i | ||||
\(543\) | −0.944265 | + | 0.944265i | −0.0405223 | + | 0.0405223i | ||||
\(544\) | −18.1079 | + | 19.2872i | −0.776368 | + | 0.826931i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 1.95409 | − | 0.449747i | 0.0836275 | − | 0.0192474i | ||||
\(547\) | 15.8895 | − | 31.1849i | 0.679385 | − | 1.33337i | −0.251429 | − | 0.967876i | \(-0.580900\pi\) |
0.930814 | − | 0.365493i | \(-0.119100\pi\) | |||||||
\(548\) | −0.710624 | + | 37.7838i | −0.0303563 | + | 1.61404i | ||||
\(549\) | − | 4.26289i | − | 0.181936i | ||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 1.11760i | − | 0.0476112i | ||||||
\(552\) | −0.257636 | + | 2.40433i | −0.0109657 | + | 0.102335i | ||||
\(553\) | 8.20329 | − | 16.0999i | 0.348839 | − | 0.684636i | ||||
\(554\) | 3.63187 | + | 15.7800i | 0.154304 | + | 0.670430i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −12.8594 | − | 6.85981i | −0.545362 | − | 0.290921i | ||||
\(557\) | −25.1416 | + | 25.1416i | −1.06528 | + | 1.06528i | −0.0675692 | + | 0.997715i | \(0.521524\pi\) |
−0.997715 | + | 0.0675692i | \(0.978476\pi\) | |||||||
\(558\) | −28.6869 | + | 11.5677i | −1.21442 | + | 0.489701i | ||||
\(559\) | −8.51896 | + | 6.18939i | −0.360314 | + | 0.261783i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 3.68905 | + | 2.68025i | 0.155752 | + | 0.113160i | ||||
\(562\) | 31.7853 | + | 7.94779i | 1.34078 | + | 0.335257i | ||||
\(563\) | −4.32450 | + | 27.3038i | −0.182256 | + | 1.15072i | 0.711674 | + | 0.702510i | \(0.247937\pi\) |
−0.893929 | + | 0.448208i | \(0.852063\pi\) | |||||||
\(564\) | −2.42419 | + | 2.33469i | −0.102077 | + | 0.0983082i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −23.1078 | + | 13.8633i | −0.971294 | + | 0.582719i | ||||
\(567\) | 20.7011 | − | 10.5477i | 0.869364 | − | 0.442963i | ||||
\(568\) | −8.08177 | − | 14.0638i | −0.339104 | − | 0.590105i | ||||
\(569\) | −8.77237 | − | 2.85032i | −0.367757 | − | 0.119491i | 0.119308 | − | 0.992857i | \(-0.461932\pi\) |
−0.487065 | + | 0.873366i | \(0.661932\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 17.2235 | − | 5.59625i | 0.720780 | − | 0.234196i | 0.0744189 | − | 0.997227i | \(-0.476290\pi\) |
0.646362 | + | 0.763031i | \(0.276290\pi\) | |||||||
\(572\) | −17.0432 | + | 22.5536i | −0.712614 | + | 0.943015i | ||||
\(573\) | 0.471166 | + | 2.97482i | 0.0196832 | + | 0.124275i | ||||
\(574\) | 1.04635 | − | 11.8674i | 0.0436737 | − | 0.495336i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 20.4834 | + | 11.9371i | 0.853475 | + | 0.497381i | ||||
\(577\) | 10.8794 | − | 1.72312i | 0.452914 | − | 0.0717345i | 0.0741898 | − | 0.997244i | \(-0.476363\pi\) |
0.378724 | + | 0.925510i | \(0.376363\pi\) | |||||||
\(578\) | −5.84010 | − | 3.65479i | −0.242916 | − | 0.152019i | ||||
\(579\) | 0.538533 | + | 1.65743i | 0.0223807 | + | 0.0688806i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −2.78310 | + | 8.56552i | −0.115463 | + | 0.355357i | ||||
\(582\) | −2.31596 | + | 1.94066i | −0.0959998 | + | 0.0804429i | ||||
\(583\) | 4.27167 | + | 8.38362i | 0.176914 | + | 0.347214i | ||||
\(584\) | −0.0500726 | + | 0.0191047i | −0.00207202 | + | 0.000790556i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 12.1209 | − | 13.9245i | 0.500709 | − | 0.575214i | ||||
\(587\) | −46.2814 | − | 7.33025i | −1.91024 | − | 0.302552i | −0.915277 | − | 0.402825i | \(-0.868028\pi\) |
−0.994960 | + | 0.100273i | \(0.968028\pi\) | |||||||
\(588\) | 0.0220445 | − | 0.0637419i | 0.000909101 | − | 0.00262867i | ||||
\(589\) | −21.7659 | + | 29.9582i | −0.896849 | + | 1.23441i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0.642112 | + | 0.883792i | 0.0264130 | + | 0.0363543i | ||||
\(592\) | −2.08608 | − | 17.3782i | −0.0857375 | − | 0.714239i | ||||
\(593\) | −11.5238 | − | 11.5238i | −0.473225 | − | 0.473225i | 0.429731 | − | 0.902957i | \(-0.358608\pi\) |
−0.902957 | + | 0.429731i | \(0.858608\pi\) | |||||||
\(594\) | 3.21811 | − | 7.56717i | 0.132041 | − | 0.310485i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −0.586763 | − | 4.21640i | −0.0240348 | − | 0.172710i | ||||
\(597\) | −4.19497 | − | 2.13745i | −0.171689 | − | 0.0874798i | ||||
\(598\) | −1.21080 | − | 17.4851i | −0.0495132 | − | 0.715019i | ||||
\(599\) | 7.21615 | 0.294844 | 0.147422 | − | 0.989074i | \(-0.452902\pi\) | ||||
0.147422 | + | 0.989074i | \(0.452902\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −15.0642 | −0.614483 | −0.307241 | − | 0.951632i | \(-0.599406\pi\) | ||||
−0.307241 | + | 0.951632i | \(0.599406\pi\) | |||||||
\(602\) | 0.994928 | + | 14.3677i | 0.0405502 | + | 0.585584i | ||||
\(603\) | 8.92939 | + | 4.54975i | 0.363633 | + | 0.185280i | ||||
\(604\) | −1.68259 | − | 12.0909i | −0.0684637 | − | 0.491971i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 1.24877 | − | 2.93641i | 0.0507280 | − | 0.119283i | ||||
\(607\) | −3.59194 | − | 3.59194i | −0.145792 | − | 0.145792i | 0.630443 | − | 0.776235i | \(-0.282873\pi\) |
−0.776235 | + | 0.630443i | \(0.782873\pi\) | |||||||
\(608\) | 28.3685 | − | 0.894649i | 1.15049 | − | 0.0362828i | ||||
\(609\) | −0.0670182 | − | 0.0922426i | −0.00271571 | − | 0.00373786i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 14.3390 | − | 19.7360i | 0.580095 | − | 0.798433i | ||||
\(612\) | −9.05976 | + | 26.1963i | −0.366219 | + | 1.05892i | ||||
\(613\) | −4.97817 | − | 0.788465i | −0.201066 | − | 0.0318458i | 0.0550888 | − | 0.998481i | \(-0.482456\pi\) |
−0.256155 | + | 0.966636i | \(0.582456\pi\) | |||||||
\(614\) | 12.0439 | − | 13.8360i | 0.486053 | − | 0.558378i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 13.7828 | + | 36.1241i | 0.555323 | + | 1.45548i | ||||
\(617\) | 8.43913 | + | 16.5627i | 0.339746 | + | 0.666790i | 0.996154 | − | 0.0876162i | \(-0.0279249\pi\) |
−0.656408 | + | 0.754406i | \(0.727925\pi\) | |||||||
\(618\) | −0.401851 | + | 0.336731i | −0.0161648 | + | 0.0135453i | ||||
\(619\) | −6.54265 | + | 20.1362i | −0.262971 | + | 0.809343i | 0.729182 | + | 0.684320i | \(0.239901\pi\) |
−0.992154 | + | 0.125024i | \(0.960099\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.57547 | + | 4.84880i | 0.0632215 | + | 0.194576i | ||||
\(622\) | 4.98960 | + | 3.12254i | 0.200065 | + | 0.125203i | ||||
\(623\) | −2.29254 | + | 0.363103i | −0.0918487 | + | 0.0145474i | ||||
\(624\) | 1.98746 | + | 0.729471i | 0.0795623 | + | 0.0292022i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −2.78279 | + | 31.5617i | −0.111223 | + | 1.26146i | ||||
\(627\) | −0.765290 | − | 4.83185i | −0.0305627 | − | 0.192966i | ||||
\(628\) | 19.5765 | − | 25.9059i | 0.781187 | − | 1.03376i | ||||
\(629\) | 19.4624 | − | 6.32373i | 0.776018 | − | 0.252144i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −3.22756 | − | 1.04870i | −0.128487 | − | 0.0417480i | 0.244068 | − | 0.969758i | \(-0.421518\pi\) |
−0.372555 | + | 0.928010i | \(0.621518\pi\) | |||||||
\(632\) | 16.5413 | − | 9.50542i | 0.657976 | − | 0.378105i | ||||
\(633\) | −3.38030 | + | 1.72235i | −0.134355 | + | 0.0684572i | ||||
\(634\) | 7.63948 | − | 4.58324i | 0.303402 | − | 0.182024i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0.507555 | − | 0.488815i | 0.0201259 | − | 0.0193828i | ||||
\(637\) | −0.0764758 | + | 0.482849i | −0.00303008 | + | 0.0191312i | ||||
\(638\) | 1.55942 | + | 0.389926i | 0.0617378 | + | 0.0154373i | ||||
\(639\) | −13.7493 | − | 9.98948i | −0.543915 | − | 0.395178i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 31.0401 | − | 22.5519i | 1.22601 | − | 0.890748i | 0.229425 | − | 0.973326i | \(-0.426315\pi\) |
0.996585 | + | 0.0825780i | \(0.0263153\pi\) | |||||||
\(642\) | 2.87003 | − | 1.15731i | 0.113271 | − | 0.0456754i | ||||
\(643\) | 6.79295 | − | 6.79295i | 0.267888 | − | 0.267888i | −0.560361 | − | 0.828249i | \(-0.689338\pi\) |
0.828249 | + | 0.560361i | \(0.189338\pi\) | |||||||
\(644\) | −21.1508 | − | 11.2828i | −0.833457 | − | 0.444604i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 7.44296 | + | 32.3388i | 0.292840 | + | 1.27235i | ||||
\(647\) | −15.4461 | + | 30.3148i | −0.607251 | + | 1.19180i | 0.358793 | + | 0.933417i | \(0.383188\pi\) |
−0.966044 | + | 0.258379i | \(0.916812\pi\) | |||||||
\(648\) | 24.3906 | + | 2.61358i | 0.958152 | + | 0.102671i | ||||
\(649\) | − | 46.2539i | − | 1.81562i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 3.77787i | 0.148066i | ||||||||
\(652\) | −0.297529 | + | 15.8196i | −0.0116521 | + | 0.619542i | ||||
\(653\) | −2.90673 | + | 5.70477i | −0.113749 | + | 0.223245i | −0.940862 | − | 0.338791i | \(-0.889982\pi\) |
0.827112 | + | 0.562036i | \(0.189982\pi\) | |||||||
\(654\) | −4.09158 | + | 0.941702i | −0.159993 | + | 0.0368235i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 7.77083 | − | 9.89096i | 0.303400 | − | 0.386177i | ||||
\(657\) | −0.0397059 | + | 0.0397059i | −0.00154907 | + | 0.00154907i | ||||
\(658\) | −12.4780 | − | 30.9445i | −0.486445 | − | 1.20634i | ||||
\(659\) | 11.5792 | − | 8.41281i | 0.451063 | − | 0.327716i | −0.338952 | − | 0.940804i | \(-0.610073\pi\) |
0.790015 | + | 0.613087i | \(0.210073\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −0.382235 | − | 0.277710i | −0.0148672 | − | 0.0108017i | 0.580327 | − | 0.814384i | \(-0.302925\pi\) |
−0.595194 | + | 0.803582i | \(0.702925\pi\) | |||||||
\(662\) | −5.55877 | + | 22.2310i | −0.216048 | + | 0.864031i | ||||
\(663\) | −0.387218 | + | 2.44480i | −0.0150383 | + | 0.0949480i | ||||
\(664\) | −7.40203 | + | 5.96923i | −0.287254 | + | 0.231651i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −9.43452 | − | 15.7257i | −0.365580 | − | 0.609360i | ||||
\(667\) | −0.887989 | + | 0.452453i | −0.0343831 | + | 0.0175190i | ||||
\(668\) | 22.1638 | − | 15.4746i | 0.857543 | − | 0.598731i | ||||
\(669\) | 2.10333 | + | 0.683413i | 0.0813193 | + | 0.0264223i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 6.98096 | − | 2.26825i | 0.269497 | − | 0.0875648i | ||||
\(672\) | 2.28779 | − | 1.77499i | 0.0882533 | − | 0.0684719i | ||||
\(673\) | −3.35456 | − | 21.1799i | −0.129309 | − | 0.816424i | −0.964038 | − | 0.265764i | \(-0.914376\pi\) |
0.834729 | − | 0.550660i | \(-0.185624\pi\) | |||||||
\(674\) | −28.4902 | − | 2.51198i | −1.09740 | − | 0.0967578i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 10.4903 | + | 1.86434i | 0.403471 | + | 0.0717055i | ||||
\(677\) | 43.8961 | − | 6.95245i | 1.68706 | − | 0.267204i | 0.762155 | − | 0.647395i | \(-0.224142\pi\) |
0.924908 | + | 0.380191i | \(0.124142\pi\) | |||||||
\(678\) | 1.16251 | − | 1.85761i | 0.0446459 | − | 0.0713410i | ||||
\(679\) | −9.25648 | − | 28.4885i | −0.355231 | − | 1.09329i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −0.916813 | + | 2.82166i | −0.0351323 | + | 0.108126i | ||||
\(682\) | −34.2075 | − | 40.8229i | −1.30987 | − | 1.56319i | ||||
\(683\) | −11.1168 | − | 21.8180i | −0.425374 | − | 0.834843i | −0.999867 | − | 0.0163335i | \(-0.994801\pi\) |
0.574493 | − | 0.818510i | \(-0.305199\pi\) | |||||||
\(684\) | 26.7458 | − | 13.0001i | 1.02265 | − | 0.497071i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −19.4986 | − | 16.9730i | −0.744460 | − | 0.648033i | ||||
\(687\) | 3.18118 | + | 0.503849i | 0.121369 | + | 0.0192230i | ||||
\(688\) | −7.40796 | + | 13.2795i | −0.282426 | + | 0.506276i | ||||
\(689\) | −3.00217 | + | 4.13213i | −0.114374 | + | 0.157422i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −9.83947 | − | 13.5429i | −0.374311 | − | 0.515195i | 0.579755 | − | 0.814791i | \(-0.303148\pi\) |
−0.954066 | + | 0.299596i | \(0.903148\pi\) | |||||||
\(692\) | −0.638571 | − | 2.09882i | −0.0242748 | − | 0.0797851i | ||||
\(693\) | 28.6452 | + | 28.6452i | 1.08814 | + | 1.08814i | ||||
\(694\) | −7.54511 | − | 3.20873i | −0.286408 | − | 0.121802i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −0.00605649 | − | 0.120230i | −0.000229571 | − | 0.00455730i | ||||
\(697\) | 13.1035 | + | 6.67656i | 0.496330 | + | 0.252893i | ||||
\(698\) | −0.0746063 | + | 0.00516630i | −0.00282389 | + | 0.000195547i | ||||
\(699\) | 5.58072 | 0.211082 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 50.9450 | 1.92417 | 0.962083 | − | 0.272757i | \(-0.0879356\pi\) | ||||
0.962083 | + | 0.272757i | \(0.0879356\pi\) | |||||||
\(702\) | 4.45307 | − | 0.308364i | 0.168070 | − | 0.0116384i | ||||
\(703\) | −19.5618 | − | 9.96723i | −0.737787 | − | 0.375921i | ||||
\(704\) | −8.64933 | + | 39.8955i | −0.325984 | + | 1.50362i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 5.35848 | + | 2.27882i | 0.201669 | + | 0.0857644i | ||||
\(707\) | 22.3682 | + | 22.3682i | 0.841244 | + | 0.841244i | ||||
\(708\) | −3.31402 | + | 1.00830i | −0.124549 | + | 0.0378942i | ||||
\(709\) | −23.6335 | − | 32.5288i | −0.887576 | − | 1.22164i | −0.974264 | − | 0.225408i | \(-0.927628\pi\) |
0.0866885 | − | 0.996235i | \(-0.472372\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 11.7492 | − | 16.1714i | 0.440629 | − | 0.606473i | ||||
\(712\) | −2.23678 | − | 1.00132i | −0.0838268 | − | 0.0375260i | ||||
\(713\) | 32.6152 | + | 5.16574i | 1.22145 | + | 0.193458i | ||||
\(714\) | 2.55355 | + | 2.22280i | 0.0955643 | + | 0.0831863i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −21.0955 | − | 43.4011i | −0.788376 | − | 1.62197i | ||||
\(717\) | −0.0396715 | − | 0.0778596i | −0.00148156 | − | 0.00290772i | ||||
\(718\) | 25.0993 | + | 29.9533i | 0.936698 | + | 1.11785i | ||||
\(719\) | −3.14270 | + | 9.67223i | −0.117203 | + | 0.360713i | −0.992400 | − | 0.123053i | \(-0.960731\pi\) |
0.875197 | + | 0.483766i | \(0.160731\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.60612 | − | 4.94314i | −0.0598152 | − | 0.184092i | ||||
\(722\) | 4.63197 | − | 7.40157i | 0.172384 | − | 0.275458i | ||||
\(723\) | 4.12192 | − | 0.652848i | 0.153296 | − | 0.0242797i | ||||
\(724\) | 2.44578 | − | 13.7619i | 0.0908966 | − | 0.511455i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 4.04805 | + | 0.356916i | 0.150237 | + | 0.0132464i | ||||
\(727\) | 1.37117 | + | 8.65722i | 0.0508538 | + | 0.321078i | 0.999981 | + | 0.00618506i | \(0.00196878\pi\) |
−0.949127 | + | 0.314893i | \(0.898031\pi\) | |||||||
\(728\) | −14.0754 | + | 15.5687i | −0.521670 | + | 0.577016i | ||||
\(729\) | 23.8224 | − | 7.74037i | 0.882312 | − | 0.286681i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −16.9084 | − | 5.49386i | −0.625378 | − | 0.203198i | ||||
\(732\) | −0.314697 | − | 0.450729i | −0.0116315 | − | 0.0166594i | ||||
\(733\) | 0.234567 | − | 0.119518i | 0.00866394 | − | 0.00441450i | −0.449653 | − | 0.893203i | \(-0.648452\pi\) |
0.458317 | + | 0.888789i | \(0.348452\pi\) | |||||||
\(734\) | −4.93920 | − | 8.23282i | −0.182309 | − | 0.303879i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −12.1957 | − | 22.1780i | −0.449538 | − | 0.817493i | ||||
\(737\) | −2.69946 | + | 17.0437i | −0.0994360 | + | 0.627814i | ||||
\(738\) | 3.19695 | − | 12.7854i | 0.117681 | − | 0.470638i | ||||
\(739\) | −5.97506 | − | 4.34113i | −0.219796 | − | 0.159691i | 0.472439 | − | 0.881363i | \(-0.343374\pi\) |
−0.692235 | + | 0.721672i | \(0.743374\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 2.14841 | − | 1.56091i | 0.0789238 | − | 0.0573415i | ||||
\(742\) | 2.61254 | + | 6.47886i | 0.0959092 | + | 0.237846i | ||||
\(743\) | 7.03452 | − | 7.03452i | 0.258071 | − | 0.258071i | −0.566198 | − | 0.824269i | \(-0.691586\pi\) |
0.824269 | + | 0.566198i | \(0.191586\pi\) | |||||||
\(744\) | −2.17920 | + | 3.34083i | −0.0798935 | + | 0.122481i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 15.8316 | − | 3.64373i | 0.579634 | − | 0.133406i | ||||
\(747\) | −4.52315 | + | 8.87719i | −0.165494 | + | 0.324799i | ||||
\(748\) | −47.7200 | − | 0.897500i | −1.74482 | − | 0.0328159i | ||||
\(749\) | 30.6785i | 1.12097i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 29.2029i | 1.06563i | 0.846232 | + | 0.532814i | \(0.178866\pi\) | ||||
−0.846232 | + | 0.532814i | \(0.821134\pi\) | |||||||
\(752\) | 6.81530 | − | 34.5624i | 0.248529 | − | 1.26036i | ||||
\(753\) | 0.470395 | − | 0.923203i | 0.0171422 | − | 0.0336434i | ||||
\(754\) | 0.195709 | + | 0.850332i | 0.00712731 | + | 0.0309673i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 2.87348 | − | 5.38664i | 0.104507 | − | 0.195910i | ||||
\(757\) | −20.1848 | + | 20.1848i | −0.733630 | + | 0.733630i | −0.971337 | − | 0.237707i | \(-0.923604\pi\) |
0.237707 | + | 0.971337i | \(0.423604\pi\) | |||||||
\(758\) | 16.7933 | − | 6.77172i | 0.609959 | − | 0.245960i | ||||
\(759\) | −3.52933 | + | 2.56421i | −0.128107 | + | 0.0930749i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 7.93313 | + | 5.76375i | 0.287576 | + | 0.208936i | 0.722215 | − | 0.691669i | \(-0.243124\pi\) |
−0.434639 | + | 0.900605i | \(0.643124\pi\) | |||||||
\(762\) | −4.20807 | − | 1.05221i | −0.152442 | − | 0.0381176i | ||||
\(763\) | 6.51124 | − | 41.1103i | 0.235723 | − | 1.48829i | ||||
\(764\) | −21.8688 | − | 22.7071i | −0.791184 | − | 0.821516i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 22.3523 | − | 13.4100i | 0.807620 | − | 0.484524i | ||||
\(767\) | 22.3715 | − | 11.3988i | 0.807788 | − | 0.411589i | ||||
\(768\) | 3.04700 | − | 0.249980i | 0.109949 | − | 0.00902038i | ||||
\(769\) | −17.2976 | − | 5.62032i | −0.623766 | − | 0.202674i | −0.0199544 | − | 0.999801i | \(-0.506352\pi\) |
−0.603812 | + | 0.797127i | \(0.706352\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 2.06162 | − | 0.669862i | 0.0742475 | − | 0.0241245i | ||||
\(772\) | −14.5531 | − | 10.9974i | −0.523778 | − | 0.395807i | ||||
\(773\) | 6.76671 | + | 42.7233i | 0.243382 | + | 1.53665i | 0.742339 | + | 0.670025i | \(0.233717\pi\) |
−0.498957 | + | 0.866627i | \(0.666283\pi\) | |||||||
\(774\) | −1.39931 | + | 15.8706i | −0.0502970 | + | 0.570455i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 8.24751 | − | 30.5323i | 0.296068 | − | 1.09604i | ||||
\(777\) | −2.21226 | + | 0.350388i | −0.0793644 | + | 0.0125701i | ||||
\(778\) | 29.8179 | + | 18.6603i | 1.06902 | + | 0.669006i | ||||
\(779\) | −4.87557 | − | 15.0055i | −0.174685 | − | 0.537626i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 9.04296 | − | 27.8314i | 0.323582 | − | 0.995884i | ||||
\(782\) | 22.6816 | − | 19.0060i | 0.811091 | − | 0.679653i | ||||
\(783\) | −0.115230 | − | 0.226151i | −0.00411798 | − | 0.00808199i | ||||
\(784\) | 0.192752 | + | 0.679133i | 0.00688401 | + | 0.0242547i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −2.41432 | + | 2.77356i | −0.0861158 | + | 0.0989297i | ||||
\(787\) | −11.9702 | − | 1.89589i | −0.426691 | − | 0.0675813i | −0.0606043 | − | 0.998162i | \(-0.519303\pi\) |
−0.366087 | + | 0.930581i | \(0.619303\pi\) | |||||||
\(788\) | −10.8064 | − | 3.73729i | −0.384961 | − | 0.133135i | ||||
\(789\) | 2.23378 | − | 3.07453i | 0.0795245 | − | 0.109456i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 12.7693 | + | 17.5755i | 0.454025 | + | 0.624911i | ||||
\(792\) | 8.80785 | + | 41.8549i | 0.312973 | + | 1.48725i | ||||
\(793\) | 2.81747 | + | 2.81747i | 0.100051 | + | 0.100051i | ||||
\(794\) | 15.4140 | − | 36.2449i | 0.547022 | − | 1.28628i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 48.8094 | − | 6.79243i | 1.73000 | − | 0.240751i | ||||
\(797\) | 14.6702 | + | 7.47486i | 0.519646 | + | 0.264773i | 0.694083 | − | 0.719895i | \(-0.255810\pi\) |
−0.174436 | + | 0.984668i | \(0.555810\pi\) | |||||||
\(798\) | −0.250912 | − | 3.62342i | −0.00888221 | − | 0.128268i | ||||
\(799\) | 41.1877 | 1.45712 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −2.56770 | −0.0907253 | ||||||||
\(802\) | 1.02202 | + | 14.7590i | 0.0360889 | + | 0.521158i | ||||
\(803\) | −0.0861499 | − | 0.0438956i | −0.00304016 | − | 0.00154904i | ||||
\(804\) | 1.28000 | − | 0.178128i | 0.0451423 | − | 0.00628210i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 11.3146 | − | 26.6055i | 0.398540 | − | 0.937139i | ||||
\(807\) | 1.36921 | + | 1.36921i | 0.0481985 | + | 0.0481985i | ||||
\(808\) | 6.87780 | + | 32.6833i | 0.241960 | + | 1.14980i | ||||
\(809\) | −12.5671 | − | 17.2972i | −0.441837 | − | 0.608136i | 0.528782 | − | 0.848757i | \(-0.322649\pi\) |
−0.970619 | + | 0.240621i | \(0.922649\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −18.5355 | + | 25.5120i | −0.650871 | + | 0.895847i | −0.999136 | − | 0.0415488i | \(-0.986771\pi\) |
0.348265 | + | 0.937396i | \(0.386771\pi\) | |||||||
\(812\) | 1.12788 | + | 0.390066i | 0.0395807 | + | 0.0136886i | ||||
\(813\) | 0.356539 | + | 0.0564703i | 0.0125044 | + | 0.00198050i | ||||
\(814\) | 20.7326 | − | 23.8176i | 0.726677 | − | 0.834806i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0.975957 | + | 3.43863i | 0.0341653 | + | 0.120376i | ||||
\(817\) | 8.65922 | + | 16.9947i | 0.302948 | + | 0.594569i | ||||
\(818\) | −16.8254 | + | 14.0988i | −0.588286 | + | 0.492953i | ||||
\(819\) | −6.79540 | + | 20.9141i | −0.237451 | + | 0.730798i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −6.22378 | − | 19.1548i | −0.217211 | − | 0.668508i | −0.998989 | − | 0.0449507i | \(-0.985687\pi\) |
0.781778 | − | 0.623557i | \(-0.214313\pi\) | |||||||
\(822\) | 4.32826 | + | 2.70867i | 0.150966 | + | 0.0944757i | ||||
\(823\) | 41.6729 | − | 6.60034i | 1.45263 | − | 0.230073i | 0.620302 | − | 0.784363i | \(-0.287010\pi\) |
0.832324 | + | 0.554289i | \(0.187010\pi\) | |||||||
\(824\) | 1.43105 | − | 5.29776i | 0.0498531 | − | 0.184556i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 3.01613 | − | 34.2082i | 0.104945 | − | 1.19026i | ||||
\(827\) | −2.15397 | − | 13.5996i | −0.0749008 | − | 0.472905i | −0.996418 | − | 0.0845669i | \(-0.973049\pi\) |
0.921517 | − | 0.388338i | \(-0.126951\pi\) | |||||||
\(828\) | −21.1571 | − | 15.9879i | −0.735261 | − | 0.555620i | ||||
\(829\) | −35.5980 | + | 11.5665i | −1.23637 | + | 0.401721i | −0.853018 | − | 0.521881i | \(-0.825230\pi\) |
−0.383352 | + | 0.923602i | \(0.625230\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 2.08074 | + | 0.676072i | 0.0721800 | + | 0.0234527i | ||||
\(832\) | −21.4277 | + | 5.64848i | −0.742872 | + | 0.195826i | ||||
\(833\) | −0.735426 | + | 0.374718i | −0.0254810 | + | 0.0129832i | ||||
\(834\) | −1.68864 | + | 1.01308i | −0.0584727 | + | 0.0350802i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 35.5203 | + | 36.8820i | 1.22850 | + | 1.27559i | ||||
\(837\) | −1.31560 | + | 8.30637i | −0.0454738 | + | 0.287110i | ||||
\(838\) | 49.5339 | + | 12.3858i | 1.71112 | + | 0.427859i | ||||
\(839\) | 6.53213 | + | 4.74587i | 0.225514 | + | 0.163846i | 0.694805 | − | 0.719198i | \(-0.255491\pi\) |
−0.469291 | + | 0.883044i | \(0.655491\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −23.4214 | + | 17.0166i | −0.807633 | + | 0.586780i | ||||
\(842\) | −21.0153 | + | 8.47419i | −0.724234 | + | 0.292040i | ||||
\(843\) | 3.13022 | − | 3.13022i | 0.107810 | − | 0.107810i | ||||
\(844\) | 18.6899 | − | 35.0362i | 0.643332 | − | 1.20600i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −8.27867 | − | 35.9698i | −0.284626 | − | 1.23667i | ||||
\(847\) | −18.2897 | + | 35.8955i | −0.628440 | + | 1.23338i | ||||
\(848\) | −1.42692 | + | 7.23635i | −0.0490008 | + | 0.248497i | ||||
\(849\) | 3.64092i | 0.124956i | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 19.5780i | 0.671126i | ||||||||
\(852\) | −2.19121 | − | 0.0412114i | −0.0750695 | − | 0.00141188i | ||||
\(853\) | 15.8344 | − | 31.0768i | 0.542160 | − | 1.06405i | −0.443652 | − | 0.896199i | \(-0.646317\pi\) |
0.985812 | − | 0.167851i | \(-0.0536826\pi\) | |||||||
\(854\) | 5.31085 | − | 1.22232i | 0.181733 | − | 0.0418271i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −17.6964 | + | 27.1294i | −0.604850 | + | 0.927265i | ||||
\(857\) | 31.7738 | − | 31.7738i | 1.08537 | − | 1.08537i | 0.0893726 | − | 0.995998i | \(-0.471514\pi\) |
0.995998 | − | 0.0893726i | \(-0.0284862\pi\) | |||||||
\(858\) | 1.42841 | + | 3.54234i | 0.0487652 | + | 0.120933i | ||||
\(859\) | −34.2690 | + | 24.8979i | −1.16924 | + | 0.849504i | −0.990918 | − | 0.134468i | \(-0.957068\pi\) |
−0.178324 | + | 0.983972i | \(0.557068\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −1.30223 | − | 0.946129i | −0.0443800 | − | 0.0322440i | ||||
\(862\) | 2.31143 | − | 9.24400i | 0.0787275 | − | 0.314852i | ||||
\(863\) | 2.60778 | − | 16.4649i | 0.0887700 | − | 0.560472i | −0.902714 | − | 0.430242i | \(-0.858428\pi\) |
0.991484 | − | 0.130230i | \(-0.0415716\pi\) | |||||||
\(864\) | 5.64826 | − | 3.10597i | 0.192158 | − | 0.105667i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −7.67388 | − | 12.7911i | −0.260769 | − | 0.434658i | ||||
\(867\) | −0.829389 | + | 0.422595i | −0.0281675 | + | 0.0143521i | ||||
\(868\) | −22.6370 | − | 32.4222i | −0.768350 | − | 1.10048i | ||||
\(869\) | 32.7340 | + | 10.6359i | 1.11043 | + | 0.360799i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −8.90876 | + | 2.89463i | −0.301862 | + | 0.0980809i | ||||
\(872\) | 29.4718 | − | 32.5986i | 0.998042 | − | 1.10393i | ||||
\(873\) | −5.18374 | − | 32.7288i | −0.175443 | − | 1.10770i | ||||
\(874\) | −31.6248 | − | 2.78836i | −1.06973 | − | 0.0943177i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −0.00126705 | + | 0.00712941i | −4.28096e−5 | + | 0.000240880i | ||||
\(877\) | −14.6759 | + | 2.32444i | −0.495571 | + | 0.0784907i | −0.399217 | − | 0.916856i | \(-0.630718\pi\) |
−0.0963539 | + | 0.995347i | \(0.530718\pi\) | |||||||
\(878\) | −7.85645 | + | 12.5541i | −0.265142 | + | 0.423679i | ||||
\(879\) | −0.770780 | − | 2.37222i | −0.0259978 | − | 0.0800129i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −15.1162 | + | 46.5230i | −0.509279 | + | 1.56740i | 0.284177 | + | 0.958772i | \(0.408280\pi\) |
−0.793456 | + | 0.608628i | \(0.791720\pi\) | |||||||
\(882\) | 0.475066 | + | 0.566939i | 0.0159963 | + | 0.0190898i | ||||
\(883\) | 0.740506 | + | 1.45332i | 0.0249200 | + | 0.0489083i | 0.903131 | − | 0.429365i | \(-0.141263\pi\) |
−0.878211 | + | 0.478274i | \(0.841263\pi\) | |||||||
\(884\) | −11.3261 | − | 23.3018i | −0.380937 | − | 0.783725i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 4.93478 | + | 4.29560i | 0.165787 | + | 0.144313i | ||||
\(887\) | 26.7206 | + | 4.23212i | 0.897189 | + | 0.142101i | 0.587963 | − | 0.808888i | \(-0.299930\pi\) |
0.309226 | + | 0.950989i | \(0.399930\pi\) | |||||||
\(888\) | −2.15845 | − | 0.966254i | −0.0724329 | − | 0.0324254i | ||||
\(889\) | 25.2757 | − | 34.7890i | 0.847719 | − | 1.16679i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 26.0125 | + | 35.8032i | 0.871452 | + | 1.19945i | ||||
\(892\) | −22.1461 | + | 6.73800i | −0.741505 | + | 0.225605i | ||||
\(893\) | −31.2456 | − | 31.2456i | −1.04560 | − | 1.04560i | ||||
\(894\) | −0.529300 | − | 0.225097i | −0.0177024 | − | 0.00752837i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −8.99834 | + | 28.9417i | −0.300614 | + | 0.966873i | ||||
\(897\) | −2.11000 | − | 1.07510i | −0.0704508 | − | 0.0358965i | ||||
\(898\) | −25.5264 | + | 1.76764i | −0.851828 | + | 0.0589870i | ||||
\(899\) | −1.64396 | −0.0548290 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −8.62349 | −0.287290 | ||||||||
\(902\) | 22.6386 | − | 1.56767i | 0.753784 | − | 0.0521976i | ||||
\(903\) | 1.73381 | + | 0.883420i | 0.0576976 | + | 0.0293984i | ||||
\(904\) | 1.15397 | + | 22.9080i | 0.0383806 | + | 0.761910i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −1.51781 | − | 0.645485i | −0.0504260 | − | 0.0214448i | ||||
\(907\) | 35.5508 | + | 35.5508i | 1.18045 | + | 1.18045i | 0.979629 | + | 0.200818i | \(0.0643600\pi\) |
0.200818 | + | 0.979629i | \(0.435640\pi\) | |||||||
\(908\) | −9.03918 | − | 29.7094i | −0.299976 | − | 0.985942i | ||||
\(909\) | 20.5690 | + | 28.3108i | 0.682230 | + | 0.939009i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 3.41319 | − | 4.69785i | 0.113084 | − | 0.155647i | −0.748723 | − | 0.662883i | \(-0.769333\pi\) |
0.861807 | + | 0.507236i | \(0.169333\pi\) | |||||||
\(912\) | 1.86823 | − | 3.34898i | 0.0618631 | − | 0.110896i | ||||
\(913\) | −16.9441 | − | 2.68368i | −0.560768 | − | 0.0888169i | ||||
\(914\) | 35.3920 | + | 30.8078i | 1.17066 | + | 1.01903i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −30.3204 | + | 14.7375i | −1.00181 | + | 0.486941i | ||||
\(917\) | −16.5498 | − | 32.4808i | −0.546522 | − | 1.07261i | ||||
\(918\) | 4.84041 | + | 5.77650i | 0.159757 | + | 0.190653i | ||||
\(919\) | −13.3369 | + | 41.0468i | −0.439944 | + | 1.35401i | 0.447990 | + | 0.894039i | \(0.352140\pi\) |
−0.887934 | + | 0.459971i | \(0.847860\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −0.765886 | − | 2.35716i | −0.0252368 | − | 0.0776709i | ||||
\(922\) | 24.2775 | − | 38.7938i | 0.799537 | − | 1.27760i | ||||
\(923\) | 15.6897 | − | 2.48500i | 0.516432 | − | 0.0817948i | ||||
\(924\) | 5.14340 | + | 0.914093i | 0.169205 | + | 0.0300714i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −43.2004 | − | 3.80897i | −1.41965 | − | 0.125171i | ||||
\(927\) | −0.899449 | − | 5.67890i | −0.0295418 | − | 0.186520i | ||||
\(928\) | 0.772396 | + | 0.995540i | 0.0253551 | + | 0.0326802i | ||||
\(929\) | −34.3019 | + | 11.1453i | −1.12541 | + | 0.365667i | −0.811829 | − | 0.583895i | \(-0.801528\pi\) |
−0.313578 | + | 0.949562i | \(0.601528\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0.842173 | + | 0.273639i | 0.0276011 | + | 0.00896814i | ||||
\(932\) | −47.8946 | + | 33.4397i | −1.56884 | + | 1.09535i | ||||
\(933\) | 0.708605 | − | 0.361052i | 0.0231987 | − | 0.0118203i | ||||
\(934\) | −11.3406 | − | 18.9028i | −0.371075 | − | 0.618520i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −18.0733 | + | 14.5748i | −0.590743 | + | 0.476394i | ||||
\(937\) | 5.92447 | − | 37.4056i | 0.193544 | − | 1.22199i | −0.679252 | − | 0.733905i | \(-0.737696\pi\) |
0.872796 | − | 0.488084i | \(-0.162304\pi\) | |||||||
\(938\) | −3.10785 | + | 12.4291i | −0.101475 | + | 0.405824i | ||||
\(939\) | 3.46333 | + | 2.51626i | 0.113022 | + | 0.0821149i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 25.8261 | − | 18.7637i | 0.841906 | − | 0.611680i | −0.0809965 | − | 0.996714i | \(-0.525810\pi\) |
0.922902 | + | 0.385034i | \(0.125810\pi\) | |||||||
\(942\) | −1.64073 | − | 4.06886i | −0.0534578 | − | 0.132571i | ||||
\(943\) | −9.94877 | + | 9.94877i | −0.323977 | + | 0.323977i | ||||
\(944\) | 22.3997 | − | 28.5110i | 0.729047 | − | 0.927954i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −26.7343 | + | 6.15307i | −0.869208 | + | 0.200054i | ||||
\(947\) | −1.60449 | + | 3.14898i | −0.0521388 | + | 0.102328i | −0.915606 | − | 0.402077i | \(-0.868288\pi\) |
0.863467 | + | 0.504405i | \(0.168288\pi\) | |||||||
\(948\) | 0.0484710 | − | 2.57720i | 0.00157426 | − | 0.0837035i | ||||
\(949\) | − | 0.0524856i | − | 0.00170375i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 1.20369i | − | 0.0390325i | ||||||
\(952\) | −35.2340 | − | 3.77551i | −1.14194 | − | 0.122365i | ||||
\(953\) | −24.4756 | + | 48.0361i | −0.792843 | + | 1.55604i | 0.0378308 | + | 0.999284i | \(0.487955\pi\) |
−0.830674 | + | 0.556759i | \(0.812045\pi\) | |||||||
\(954\) | 1.73331 | + | 7.53101i | 0.0561179 | + | 0.243825i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0.807001 | + | 0.430491i | 0.0261003 | + | 0.0139231i | ||||
\(957\) | 0.153571 | − | 0.153571i | 0.00496426 | − | 0.00496426i | ||||
\(958\) | 9.13605 | − | 3.68402i | 0.295172 | − | 0.119025i | ||||
\(959\) | −40.9512 | + | 29.7528i | −1.32238 | + | 0.960767i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 18.9882 | + | 13.7957i | 0.612523 | + | 0.445024i | ||||
\(962\) | 16.6292 | + | 4.15806i | 0.536146 | + | 0.134061i | ||||
\(963\) | −5.30901 | + | 33.5198i | −0.171080 | + | 1.08016i | ||||
\(964\) | −31.4630 | + | 30.3014i | −1.01336 | + | 0.975943i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −2.77741 | + | 1.66628i | −0.0893618 | + | 0.0536118i | ||||
\(967\) | −13.8004 | + | 7.03165i | −0.443791 | + | 0.226123i | −0.661582 | − | 0.749873i | \(-0.730115\pi\) |
0.217792 | + | 0.975995i | \(0.430115\pi\) | |||||||
\(968\) | −36.8796 | + | 21.1928i | −1.18535 | + | 0.681163i | ||||
\(969\) | 4.26415 | + | 1.38551i | 0.136984 | + | 0.0445089i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −16.7721 | + | 5.44959i | −0.538242 | + | 0.174886i | −0.565508 | − | 0.824743i | \(-0.691320\pi\) |
0.0272659 | + | 0.999628i | \(0.491320\pi\) | |||||||
\(972\) | 6.12014 | − | 8.09889i | 0.196303 | − | 0.259772i | ||||
\(973\) | −3.05393 | − | 19.2817i | −0.0979044 | − | 0.618144i | ||||
\(974\) | −2.59016 | + | 29.3769i | −0.0829940 | + | 0.941295i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 5.40154 | + | 1.98256i | 0.172899 | + | 0.0634602i | ||||
\(977\) | −52.0437 | + | 8.24291i | −1.66502 | + | 0.263714i | −0.916687 | − | 0.399605i | \(-0.869147\pi\) |
−0.748337 | + | 0.663319i | \(0.769147\pi\) | |||||||
\(978\) | 1.81219 | + | 1.13408i | 0.0579473 | + | 0.0362640i | ||||
\(979\) | −1.36625 | − | 4.20489i | −0.0436656 | − | 0.134389i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 14.2286 | − | 43.7910i | 0.454283 | − | 1.39814i | ||||
\(982\) | −5.33297 | + | 4.46875i | −0.170182 | + | 0.142603i | ||||
\(983\) | 7.96803 | + | 15.6381i | 0.254141 | + | 0.498779i | 0.982463 | − | 0.186455i | \(-0.0596999\pi\) |
−0.728323 | + | 0.685234i | \(0.759700\pi\) | |||||||
\(984\) | −0.605826 | − | 1.58785i | −0.0193130 | − | 0.0506188i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −0.967261 | + | 1.11119i | −0.0308039 | + | 0.0353875i | ||||
\(987\) | −4.45259 | − | 0.705221i | −0.141728 | − | 0.0224474i | ||||
\(988\) | −9.08498 | + | 26.2693i | −0.289032 | + | 0.835736i | ||||
\(989\) | 9.99752 | − | 13.7604i | 0.317903 | − | 0.437555i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −20.0939 | − | 27.6568i | −0.638302 | − | 0.878548i | 0.360221 | − | 0.932867i | \(-0.382701\pi\) |
−0.998524 | + | 0.0543192i | \(0.982701\pi\) | |||||||
\(992\) | −1.31600 | − | 41.7293i | −0.0417832 | − | 1.32491i | ||||
\(993\) | 2.18931 | + | 2.18931i | 0.0694756 | + | 0.0694756i | ||||
\(994\) | 8.50278 | − | 19.9937i | 0.269692 | − | 0.634161i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0.177087 | + | 1.27252i | 0.00561122 | + | 0.0403214i | ||||
\(997\) | −1.87335 | − | 0.954518i | −0.0593295 | − | 0.0302299i | 0.424074 | − | 0.905628i | \(-0.360600\pi\) |
−0.483404 | + | 0.875398i | \(0.660600\pi\) | |||||||
\(998\) | 1.93576 | + | 27.9542i | 0.0612754 | + | 0.884875i | ||||
\(999\) | −4.98610 | −0.157753 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 500.2.l.e.43.8 | 96 | ||
4.3 | odd | 2 | inner | 500.2.l.e.43.7 | 96 | ||
5.2 | odd | 4 | 100.2.l.b.87.1 | yes | 96 | ||
5.3 | odd | 4 | 500.2.l.f.207.12 | 96 | |||
5.4 | even | 2 | 500.2.l.d.43.5 | 96 | |||
15.2 | even | 4 | 900.2.bj.d.487.12 | 96 | |||
20.3 | even | 4 | 500.2.l.f.207.1 | 96 | |||
20.7 | even | 4 | 100.2.l.b.87.12 | yes | 96 | ||
20.19 | odd | 2 | 500.2.l.d.43.6 | 96 | |||
25.2 | odd | 20 | inner | 500.2.l.e.407.7 | 96 | ||
25.11 | even | 5 | 100.2.l.b.23.12 | yes | 96 | ||
25.14 | even | 10 | 500.2.l.f.343.1 | 96 | |||
25.23 | odd | 20 | 500.2.l.d.407.6 | 96 | |||
60.47 | odd | 4 | 900.2.bj.d.487.1 | 96 | |||
75.11 | odd | 10 | 900.2.bj.d.523.1 | 96 | |||
100.11 | odd | 10 | 100.2.l.b.23.1 | ✓ | 96 | ||
100.23 | even | 20 | 500.2.l.d.407.5 | 96 | |||
100.27 | even | 20 | inner | 500.2.l.e.407.8 | 96 | ||
100.39 | odd | 10 | 500.2.l.f.343.12 | 96 | |||
300.11 | even | 10 | 900.2.bj.d.523.12 | 96 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
100.2.l.b.23.1 | ✓ | 96 | 100.11 | odd | 10 | ||
100.2.l.b.23.12 | yes | 96 | 25.11 | even | 5 | ||
100.2.l.b.87.1 | yes | 96 | 5.2 | odd | 4 | ||
100.2.l.b.87.12 | yes | 96 | 20.7 | even | 4 | ||
500.2.l.d.43.5 | 96 | 5.4 | even | 2 | |||
500.2.l.d.43.6 | 96 | 20.19 | odd | 2 | |||
500.2.l.d.407.5 | 96 | 100.23 | even | 20 | |||
500.2.l.d.407.6 | 96 | 25.23 | odd | 20 | |||
500.2.l.e.43.7 | 96 | 4.3 | odd | 2 | inner | ||
500.2.l.e.43.8 | 96 | 1.1 | even | 1 | trivial | ||
500.2.l.e.407.7 | 96 | 25.2 | odd | 20 | inner | ||
500.2.l.e.407.8 | 96 | 100.27 | even | 20 | inner | ||
500.2.l.f.207.1 | 96 | 20.3 | even | 4 | |||
500.2.l.f.207.12 | 96 | 5.3 | odd | 4 | |||
500.2.l.f.343.1 | 96 | 25.14 | even | 10 | |||
500.2.l.f.343.12 | 96 | 100.39 | odd | 10 | |||
900.2.bj.d.487.1 | 96 | 60.47 | odd | 4 | |||
900.2.bj.d.487.12 | 96 | 15.2 | even | 4 | |||
900.2.bj.d.523.1 | 96 | 75.11 | odd | 10 | |||
900.2.bj.d.523.12 | 96 | 300.11 | even | 10 |